All Questions
5,185 questions
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on reductive monoids which are gorenstein
Let $M$ a reductive monoid, i.e. a integral normal affine scheme, which is a monoid whose group of units is a connected reductive group.
By Rittatore http://www.cmat.edu.uy/cmat/docentes/alvaro/...
- 3,472
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0
answers
65
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The topology of complete minimal surfaces of finite total Gaussian curvature [closed]
Suppose that M is
a complete minimal surface with finite total curvature. If M is embedded in $\mathbf{R}^3$, then
we observe that M viewed from infinity looks like a plane passing through the ...
- 11
1
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0
answers
130
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Regarding graphs of continuous functions between zero dimensional spaces
Background for the question: Let for any topological space $B$, $I(B)$ denote the topological space which has the same set of points as of $B$, and the topology is generated by closed and open sets of ...
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92
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Tubular neighbourhood which is nowhere piecewise linear
I recently asked this question.
I think, if the following were true, then I would solve my problem.
Let $E\subset\{(x_1,\dots,x_n)\in\mathbb R^n\;|\;x_i\geq 0\, \&\, \sum_ix_i=1\}$ be a convex ...
- 11
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0
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331
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Relationship between weak Lp and strong Lq topologies for q<p
Specificaly:
Does convergence in $L^{\frac{1}{2}}$ imply weak $L^2$ convergence?
Having a limit in $L^{\frac{1}{2}}$ topology and a limit in weak $L^2$ topology whether these are always equal? If not,...
- 203
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83
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Topologies on spaces of linear sections
Let $X$ and $Y$ be topological linear spaces which are complete & Hausdorff, and admit dual spaces which separate points. Suppose the topologies are non-separable and non-metrizable.
Let $f : X \...
- 8,512
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75
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Collapsing a countable collection of intervals on $\mathbb{S}^1$
Consider a countable collection $I_n$ of closed connected disjoint intervals on $\mathbb{S}^1$. When this collection is maximal, the set $\bigcap \nolimits_{i=1}^{n}( \mathbb{S}^1 \backslash \bigcup \...
- 541
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167
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How many ways we have to prove that a topologically (or analytically) nice mapping is injective?
I would like to know what are the methods people have used to prove that a topologically (or analytically) nice mapping $f: B\to \Omega$ is injective? Above, $B$ is the unit ball in $\Bbb R^n$ and $\...
- 1,881
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0
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479
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Comparing two metrics on the space of infinite sequences and relating open and closed sets
Let $X = \{ 0, 1 \}$ and $X^{\mathbb N_0} = \{ x_0 x_1 x_2 \ldots : x_i \in X \}$ be the space of all infinite sequences, then a metric could be defined on it
$$
d(u,v) := \frac{1}{2^r} \mbox{ with } ...
- 798
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226
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The image of homomorphism of fundamental group of closed surface [closed]
$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed orientable surface $S$ of genus >=2. If $\phi$ is not an epimorphism, can we find a non-surjective self map $f: S\to S$ ...
- 21
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663
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Extending a homeomorphism from a dense set [closed]
Let $X$ and $Y$ be Hausdorff topological spaces, and let $f : X \to Y$ be a Borel-measurable function. Suppose that $D \subseteq X$ is dense, that the image $f(D) \subseteq Y$ is dense, and that $f$ ...
- 8,512
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178
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Proving that two given functionally structured spaces are isomorphic
The relevant definitions are listed below. They can be found in Chapter VI, pages 297-298 of Bredon's Introduction to Compact Transformation Groups; and Section 2, Chapter II of Bredon's Topology and ...
- 111
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1
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163
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Precompact reflection in diagonal uniform spaces
Each diagonal uniform space $(X,\mathcal D)$ can be derived from the covering uniform space $(X,\Sigma_{\mathcal D})$ and each covering uniform space $(X,\Sigma)$ can be derived from the diagonal ...
user31967
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70
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Orbit spaces of involutions on spheres
I'm studying the following problem: Let
$({\mathbb S}^N,\theta)$ be the $n$-sphere (in ${\mathbb R}^{N+1}$) endowed with the antipodal action $\theta:(x_0,\ldots,x_N)\to (-x_0,\ldots,-x_N)$;
$({\...
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130
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A question on star $\sigma$-compact spaces
The question is also posted here.
A topological space $X$ is said to be star $\sigma$-compact if whenever $\mathscr{U}$ is an open cover of $X$, there is a $\sigma$-compact subspace $K$ of $X$ such ...
- 654
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0
answers
275
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Regular Borel Measures equivalent definition
Please help me understand how the below definition is equivalent to the standard definition of regularity which says that a measure is regular if for which every measurable set can be approximated ...
- 11
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145
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Reference needed: Does pseudo laminated compact subsets of the plane separate the plane?
Hi,
doing my research I found the following problem and I´ll be glad if someone could give a reference.
We say that a compact connected subset $K$ of the plane is psuedo laminated if the following ...
- 19
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321
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Type I subspaces of the Stone Cech compactification of $\omega$
EDIT: I found a construction, see below. I decided not to delete the question in case someone is interested.
A space $X$ is of Type I if $X=\cup_{\alpha<\omega_1} X_\alpha$, where each $X_\alpha$ ...
- 1,855
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430
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Intersection of cocompact closed normal subgroups
Let $G$ be a locally compact Hausdorff topological group.
Definition A closed normal subgroup $H \unlhd G$ is called cocompact if $G/H$ is compact with respect to the quotient topology.
Note that ...
- 1,498
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264
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Z-sets in the Hilbert cube
If $(X,d)$ is a metric space, then we say that a closed subset $A$ of $X$ is a z-set if for each number $k\gt 0$ there is a continuous map $f_k$ from $X$ into $X-A$ such that $d(x,f_k(x))\lt k$.
I ...
- 11
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245
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Sums of Strongly z-ideals
In the rings of continuous functions,i.e.$(C(X))$ an ideal $I$ is called strongly $z$-ideal if it is an intersection of some maximal ideals of $C(X)$. i.e. $$I=\cap_{\alpha \in A} \mathcal{M_{\alpha}}$...
- 1,788
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169
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Algebraic properties of the semiring of open subsets.
Does anyone know of a useful general topological application of the algebraic properties of the semiring of open subsets of some topological space? Or examples of any such nontrivial properties at all?...
- 3,513
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315
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Non trivial definition of bicontinuous functions and the ring of all bicontinuous functions.
At first let me recall that if There are two topology $\tau_1$and $\tau_2$ on a set $X$, the triple $(X,\tau_1,\tau_2)$ is called a bitopological space.
There are many definitions and properties ...
- 1,788
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365
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Killing homotopy groups by removing subsets
Let $X$ be a locally finite CW-complex and let $U$ be an open subset of $X$. Given a non-zero homotopy class $x\in\pi_i(U)$ say, is it possible to find a closed subset $Z\subset U$ whose removal from $...
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1
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217
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F-spaces and points whose complements are C*-embedded
Let $X$ be a compact Hausdorff space. If $X$ is extremally disconnected then the complement of every point $x$ in $X$ is C*-embedded in $X$ (i.e every continuous bounded real-valued function on $X\...
- 607
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202
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Soft sheaves on indiscrete paracompact spaces
Let $X$ be some space, I have basically 2 questions:
1 - Are sheaves on paracompact but not Hausdorff spaces acyclic? I've been doing some reading and some authors say that soft sheaves on ...
- 417
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430
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Universal Hausdorff Space [duplicate]
Possible Duplicate:
Largest Hausdorff quotient
Is there a left adjoint to ${\mathbf{Haus}}\to{\mathbf{Top}}$? Here ${\mathbf{Haus}}$ is the full subcategory of Hausdorff spaces in ${\mathbf{Top}}$...
user2529
1
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0
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267
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subset embedding gives trefoil knot [closed]
Let $X$ be a topological space and $E_n(X)$ the space of finite sets of cardinality $\leq n$.
It is a theorem of Bott that $E_3(S^1)=S^3$. What is the idea to show that
the embedding $S^1\...
- 11
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150
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Follow up question on the measure of the difference between a partial selector and a selector...
This is a different question from my previous question Difference between a partial selector and a selector, however I am going to repeat the preamble...
In Kharazishvili's "Nonmeasurable Sets and ...
- 463
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220
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Extension of homeomorphisms on a spherical space
Call a "blot" set, which is the closure of its interior, the boundary is locally connected, and when you remove boundary blot remains connected. Suppose that there is a blot on the surface of the n-...
- 181
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10
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9k
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What is an explicit example of a sequence converging to two different points? [closed]
In principle a sequence in a non-Hausdorff space can converge to two points simultaneously.
Can anyone give me an explicit example of the above?
Or tell me any method of generating such kinds of ...
- 3,541
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4
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746
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A question on metrizable space
Q1, Does a metrizable space $X$ with $e(X)=\omega$ (i.e., it has countable extent) which is not lindelof exist?
Q2, Let $X$ be the one point lindefication of a discret space of cardinality $\omega_1$...
- 654
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3
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384
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Existence of a Sub-Category of the Category of Topological Spaces
My question start with the following observations:
If you have a finite number of topological spaces $X_1, \dots , X_n$ you can define a space that is the disjoint union of its $\sqcup_{i=1}^n X_n=Y$....
- 335
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1
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176
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What does mean by "$\omega +1$ is convergent sequence"? [closed]
Let $X=\omega +1$ be convergent sequence. Then what does mean by "$X$ is convergent sequence"?
- 505
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1
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882
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What does the 3rd axiom of topologies defined by neighbourhood mean? [closed]
Recall the axioms of a topology defined in terms of neighbourhoods, we call a topology on $X$ a family $(\mathcal{V}_x)_{x\in X}$ of sets in $\mathcal{P}(\mathcal{P}(X))$ which verifies for all $x\in ...
- 131
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521
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Extremely disconnected space
A topological space $X$ is called relative extremely disconnected if it has a base $B$(for open subsets) such that disjoint elements in B have disjoint closure, i.e, if $C, D$ in $B$ and $C\cap D=\...
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1
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178
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Borel subsets of Polish groups
Suppose that I have a polish group $G$ and two subsets $A$ and $B$ of $G$ such that: $A$ is open in $G$ and $B$ is closed in $G,$ from this, can I conclude that $AB$ is a Borel subset of $G$? if not, ...
- 313
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605
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Is there a continuous surjection $\omega^\omega\to \mathbb{R}$? [closed]
Let $\omega$ be endowed with the discrete topology, and let $\mathbb{R}$ carry the Euclidean topology. Is there a continuous surjective map $f:\omega^\omega\to \mathbb{R}$?
(I suppose this would ...
- 48.9k
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2
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548
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A question about locally compact spaces
Recently I read a book about linear algebraic group written by Ian Macdonald. There is a conclusion which I can't prove.
It says that if $X$ is locally compact Hausdorff space, then $X$ is compact if ...
- 89
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277
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Are knot invariants topological invariants? [closed]
I am a bit confused about terminology considering topology and knot theory.
A topological invariant is considered to be a topological property that does not change under a homeomorphism of the space.
...
- 1,465
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2
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348
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If a graph embedded on a surface is divided by a curve into a right and left that do not intersect can it be embedded on a surface of smaller genus?
Suppose we have a graph $G$ embedded on a (smooth, orientable etc) surface $Q$. Suppose there is a cycle $C$ of $G$ such that
$C$ does not separate our surface $Q$ into two connected regions and ...
- 111
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327
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Can we generalise groupoids to monoid-oids? [closed]
Groups correspond to one object categories where every morphism is an isomorphism. Monoids correspond to one object categories.
Groupoids correspond to small categories where every morphism is an ...
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1
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133
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"Universal" connected spaces
Let $\kappa$ be an infinite cardinal. Does there exist a topology $\tau_{\kappa+1}$ on $\kappa+1$ such that for any topological space $(X,\tau)$ with $|X|=\kappa$ the following statement is true?
...
- 48.9k
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501
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0
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474
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Hilbert space having all norms (and seminorms) continous.
Suppose I have a Hilbert space $H$ such that every seminorm on $H$ is continuous with respect to the inner-product induced norm. Is $H$ necessarily finite-dimensional? If not, is there an easy ...
- 617
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3
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238
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Extending $\mathbb{R}$ to a higher dimensional manifold [closed]
If a topological space $X$ is Hausdorff, connected, second countable, homogeneous (i.e. it has transitive homeomorphism group) and embeds the real line $\mathbb{R}$, does it follow that $X$ is a ...
0
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1
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152
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Name for a monoid on the basis of a vector space?
Is there a name for the structure of a vector space with a monoid defined on its basis?
Given a vector space V over a field F, we can choose a basis and define a monoid on it. Now we can use each ...
- 481
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2
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199
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Give an example of a Rothberger space $X$ which has a Lindelöf subspace $Y$ that is not Rothberger
A space $X$ is said to be Rothberger if for each sequence $(\mathcal{U}_n)$ of open covers of $X$ there exists a sequence $(U_n)$ such that for each $n$ $U_n\in\mathcal{U}_n$ and $\{U_n : n\in\mathbb{...
- 505
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1
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377
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How to prove that there does not exist any plane isotopy from the logarithmic spiral onto the real line? [closed]
Questions.
EDIT: readers please note that while this question arose in research, the OP was so hung-up on a question concerning infinite planar graphs that a strong a-forteriori-reason, kindly ...
- 6,051
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1
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177
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$Ax=b$ in a function space
Let
$X$ be compact Hausdorff topological space,
$C(X)$ denote the algebra of complex-valued continuous functions on $X$,
$b\in \mathbb{C}^m$,
$\mathbf{A}\in C(X)^{m\times n}$,
for all $x\in X$, $b\...
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