All Questions
5,184 questions
0
votes
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114
views
Recontruction of the weak topolgy from the scalar product on a subset of a Hilbert Space
Let $M$ be a set a let $K:M\times M\to\mathbb{C}$ be a positive definite kernel. By a version of Moore-Aronszajn Theorem, there is a unique (up to the unitary euivalence) Hilbert Space $X$, and a map $...
- 5,529
5
votes
1
answer
301
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Lebesgue dimension of closures satisfying the Z-set condition
Given any subspace $A\subset X$ of a topological space with Lebesgue dimension $\le N$.
Let $\bar{A}$ denote the closure of $A$. Assume, that the pair $(\bar{A},A)$ satisfies the Z-set condition, i....
- 11.1k
4
votes
2
answers
607
views
Invertible elements in monoid rings of unital monoids without non-trivial invertible elements
This question is somewhat related to Tilmans notorious problem in this post. Let $(M,\cdot)$ be a monoid with unit $1$ and set
$$(M,\cdot)^{\times} := \lbrace x \in M \mid \exists y \in M : xy=yx=1 \...
- 25.5k
1
vote
0
answers
137
views
(The Homotopy type of the) lifting of homeomorphism of Grassmanian
For $k<n$ put $FM_{k\times n}$ for the space of all $k\times n$ full rank matrices with real or complex entries. Note that the permutation group $S_{n}$ has an obvious action on this space ...
- 366
0
votes
0
answers
161
views
question about the tightness of probability measures for a general topological space
Let $(E,\mathcal{X})$ be a topological space and denote by $\mathcal{F}$ its collection of Borel subsets referred to $\mathcal{X}$. Now let $\mathcal{P}$ be the set of all probabilities on $(E,\...
- 1,835
1
vote
1
answer
164
views
The proper name for a kind of ordered space [closed]
I'm trying to find the correct term for a specific kind of totally ordered space:
Let $S$ be a totally ordered space with strict total order $<$.
Property: For any two $s_{1}$ and $s_{2}$ in $S$ ...
- 121
3
votes
1
answer
401
views
Action on a compact group
If $G$ is an infinite compact group, how many orbits can $G$ have under the group action of its continuous automorphisms ?
- 1,555
2
votes
3
answers
1k
views
Baire category theorem
Let's call the following conditions (1): $X$ is a complete metric space with metric $d$, $X = \cup_{n=1}^\infty A_n$. Let $\bar{A}$ denote the closure of $A$.
Let's call the following statement (2): ...
- 498
5
votes
1
answer
1k
views
Equivalence of boundedness and total boundedness
Compact subspaces of metric spaces are totally bounded. In some spaces, however, this is equivalent to just being bounded. This (supposedly) holds in finite dimensional Banach spaces.
Can we ...
- 2,389
3
votes
1
answer
524
views
Metrizable implies hemicompact
In the paper
R. Arens: A Topology for Spaces of Transformations, Ann. of Math. 47(1946), 480-495
the author states in the introduction that if $B$ is a metric space and the space of continuous ...
- 16.2k
0
votes
0
answers
208
views
A noncommutative analogy of the tube lemma
Assume that $A$ and $B$ are two unital commutative Banach algebras. Assume that $\phi \in \mathcal{M} (A)$ is an element of the maximal Ideal space. Define $\alpha: A\hat{\otimes} B \to \mathbb{C}\...
- 366
0
votes
1
answer
360
views
Triviality of finite fiber bundles [closed]
Hello,
I suspect the following is true and easy but I am unable to prove. Suppose (E, B, π, F) is a fiber bundle, where E,B are compact and F is finite, prove that E is a trivial fiber bundle. Any ...
5
votes
2
answers
1k
views
Relating Euler characteristic, intersection product, Morse theory (plus SU(2) and 3-manifolds)
Suppose we have a (closed, oriented) 3-manifold M with a Heegard surface F of genus g. Let F* denote F with a puncture. Then the space H of representations of pi_1(F*) on SU(2) is just SU(2)^2g, and ...
- 1,129
2
votes
2
answers
312
views
on $F_\sigma$-discrete space
A space is $F_\sigma$-discrete space if it is the countable union of closed discrete subspaces. Is it true that every subset of an $F_\sigma$-discrete space is of the type $G_\delta$?
- 654
2
votes
1
answer
384
views
Properties of the weak-$*$ topology
Let $X$ be a topological affine space over a complete base field $\mathbb S := \mathbb C$, $\mathbb R$ or $\mathbb Q_p$. Let $X^*$ be the dual space of continuous affine functionals equipped with the ...
3
votes
1
answer
228
views
Product of Topological Measure Spaces
Def. A Radon measure $\mu$ on a compact Hausdorff space $X$ is uniformly regular if there is a countable family $\mathcal{A}$ of compact $G_\delta$-subsets of $X$ such that for every open set $U\...
- 103
3
votes
0
answers
174
views
Number of k-generated semigroups
Given some $k>1$, I am interested in the number of $k$-generated semigroups of order $n$ (either up to isomorphism or all associative binary operations on an n-element set). At first I thought $3$-...
- 53
6
votes
1
answer
405
views
Infinite closed partition of the real line with no closed infinite unions
Is there a partition of the real line into infinitely many closed subsets so that no infinite union of these subsets (except the whole space) is closed?
This question was asked also at math....
- 367
3
votes
3
answers
471
views
Lebesgue dimension of images
Given a map of topological spaces $f:X\rightarrow Y$. Assume, that $X$ has finite Lebesgue dimension. I am wondering, what dim$(f(X))$ might be. Of course, if $f$ is a homeomorphism onto its image, ...
- 11.1k
3
votes
1
answer
261
views
Does the "measure-preserving property" commute with ultralimits ?
Let $(X, \mathcal{B}, \mu, T)$ be a measure-preserving system, with $T$ invertible, where the $\sigma$-algebra $\mathcal{B}$ is a Borel algebra arising from a topology which makes $T$ continuous, and ...
- 7,249
2
votes
1
answer
226
views
A question on countably compact space
A regular space $X$ is
star compact (which implies pseudocompact)
with $G_\delta$-diagonal
star countable
first countable
$e(X)\le \aleph_0$ ( in fact it implies star countable)
$|X|=\aleph_1$
Cech-...
- 654
4
votes
1
answer
860
views
Does pushforward preserve outer regularity?
(ZF + Countable Choice)
Let $\langle A,\mathcal{S} \hspace{.02 in} \rangle$ and $\langle B,\mathcal{T} \hspace{.06 in} \rangle$ be second-countable Hausdorff spaces.
Let $\Sigma$ be a sigma-algebra ...
user5810
2
votes
1
answer
1k
views
Lebesgue covering dimension
Roughly from wikipedia: The covering dimension of a topological space $X$ is defined to be the minimum value of $n$ such that every finite open cover of $X$ has a finite open refinement in which no ...
- 6,034
0
votes
1
answer
163
views
Existence of half-planes with respect to regular open sets of the Euclidean plane
I initially asked this question at math.stackexchange.com but there was no reaction, so I thought this may be a good idea to transfer it to mathoverflow.net
Let $\langle\mathrm{r}\mathscr{O},\mathord{...
- 1,112
2
votes
0
answers
184
views
The mathematics in understand anyons [closed]
I've been about particles called anyons which exist within a two dimensional framework. I've also found out that these particles can have an angular momentum equal to any real number. Normally, in ...
5
votes
1
answer
401
views
Topological space associated to a real or complex scheme
Hi, consider a scheme $X$ of finite type over $\mathbb{R}$ (or $\mathbb{C}$). In Hartshorne's appendix B on 'transcendental methods' it is shortly mentioned how to assign a reasonable topological ...
- 103
4
votes
1
answer
607
views
Topological Groups and Families of Pseudometrics
The topology on a topological group is generated by a family of pseudometrics. The only proof I know passes through uniform spaces (by which I mean the entourage definition): A topological group has ...
- 6,870
5
votes
1
answer
1k
views
Do continuous maps give continuity in the 'topology' of Hausdorff distance?
I was reading this question:
limiting behaviour of converging loops on a torus
And I wanted to be able to give an argument along the lines of: "If your loops are converging in your torus, their ...
- 3,230
2
votes
0
answers
99
views
Equicontinuity of $\{f_{2n}\circ f_{2n-1}\}$
Let $(X,D)$ be a compact metric space and $\{f_n\}_{n\in\mathbb{N}}$ be a sequence of homeomorphisms of $(X,d)$. It is easy to see that if $\{f_n\}$ is uniformly convergent then $\{g_n\}$ defined by $...
3
votes
1
answer
83
views
Cosets of the fixer of an action of a monoid on a finite set
Let $M$ be a monoid that acts transitively from the right on a finite set $X$.
Assume furthermore that the action of $M$ on $X$ induces for every $m \in M$ a bijection on $X \to X, x \mapsto x.m$.
Let
...
- 77
1
vote
0
answers
99
views
Name for condition on map of cancellative monoids
Let $M,N$ be cancellative monoids with identity $\epsilon$ and suppose that $k\colon M\rightarrow N$ is a function such that
$k(\epsilon)=\epsilon$
for all $a,b\in M$, there exists $v\in N$ such that ...
3
votes
0
answers
171
views
Berkovich Analytification of the transseries
I am looking for references to articles about the following subjects:
Connections from the field of (real) transseries to the field of surreal numbers (mentioned very briefly in the introduction of ...
- 161
4
votes
0
answers
330
views
determine if a toric variety is Gorenstein
Let $G$ a simply connected group over $k$ and $car(k)=0$.
Let $T_{+}=(T\times T)/Z_{G}$ we consider the closure $\overline{T}_{+}$ of the torus $T_{+}$ in $\prod End(V_{\omega_{i}})\times\prod\...
- 3,472
4
votes
1
answer
671
views
Sections of an etale space
In R.O.Wells book "Differential Analysis on Complex Manifolds" p. 44 proof of Theorem 2.2 part b) the author claims that any two sections of an etale space which agree at a point agree in some ...
- 43
-2
votes
1
answer
458
views
some trouble over the cardinality of the cantor set(middle one-thirds) [closed]
firstly i thank you for taking interest in my post but i am new here so if i have made some mistakes or done something which is out of place please point out.my problem is-
we know that the cantor ...
- 19
2
votes
0
answers
96
views
On compactness in $C(X)$
Let $X$ be a Tychonoff space. It is well known, that for a family of scalar functions equicontinuity + pointwise boundedness imply relative compactness in $C(X)$ (with compact-open topology). It is ...
- 5,529
0
votes
1
answer
237
views
How to see such space is Lindelof?
Let $R$ denote the set of all real numbers. $B$ is any Bernstein set of $R$.
Bernstein Set: A subset of the real line that meets every uncountable closed subset of the real line but that contains ...
- 654
2
votes
1
answer
245
views
Assumptions on a commutative C*-algebra to get a nice C(X) - space
I have the following question,
Is it possible to get somehow a compact Hausdorff space $X$ which is second-countable from a unital commutative C*-algebra. If it is possible, what should we assume ...
- 145
16
votes
1
answer
567
views
Do strict pro-sets embed in locales?
It is well-known that the category of profinite groups (by which I mean Pro(FiniteGroups), i.e. the category of formal cofiltered limits of finite groups) is equivalent to a full subcategory of ...
- 66.8k
1
vote
2
answers
405
views
Cardinality of the set of countable dense subgroups of the reals up to isomorphism.
Joel David Hamkins in an answer to my question Countable Dense Sub-Groups of the Reals points out that "one can find an uncountable chain of countable dense additive subgroups of $\mathbb{R}$ whose ...
- 463
2
votes
1
answer
296
views
Methods to tell if a magma has idempotents
(Disclaimer: below, when I say "compact" I mean "compact Hausdorff.")
I asked a version of this question on math stackexchange (https://math.stackexchange.com/questions/305186/left-continuous-magmas-...
- 20.5k
0
votes
2
answers
370
views
zeroset-diagonal
Is it true that a topology space X with a zeroset diagonal is first countable?
what if X is additionally CCC?
- 654
6
votes
2
answers
497
views
Can I detect the point of impact without looking at it?
I'm going to postpone the motivation for this question because the question itself involves no complicated maths and may well have a very simple solution so I don't want to put anyone off with high ...
- 26.8k
2
votes
1
answer
104
views
Separating Differences of Open Sets
Has anyone ever considered something like the following separation axiom?
$(*)$ For any pair of open sets $O$ and $N$, there exist disjoint open sets containing $O\setminus N$ and $N\setminus O$.
...
- 1,307
3
votes
3
answers
728
views
What do you call the product of a circle and an annulus?
What would you call the product of an annulus and $S^1$ (a 'thickened' torus like 3-manifold)?
More generally, is there an archive or list online of names assigned to various (non-standard) manifolds ...
- 3,165
5
votes
0
answers
70
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Does the $D$-property have universal objects?
A space $(X,\tau)$ is called a $D$-space if whenever one is given a neighborhood $N(x)$ of $x$ for each $x\in X$, then there is a closed discrete subset $D\subseteq X$ such that $\{N(x): x\in D\}$ ...
- 48.9k
4
votes
0
answers
90
views
Topological systems of imprimitivity
Let $G$ be a group acting by homeomorphisms on a topological space $X$. $G$ is topologically transitive if every open $G$-invariant subset of $X$ is empty or dense.
Here is an attempt to define ...
- 4,728
1
vote
1
answer
182
views
A space with countable tightness which is not a Fréchet space?
I need a space with countable tightness which is not a Fréchet space. In this space, I am searching for a point with no deleted neighborhood consisting entirely of P-points.
(A P-point is a point $x \...
- 113
4
votes
0
answers
199
views
Correspondence between numerical semigroups and polynomials?
A numerical semigroup $A$ is defined as a subsemigroup of the semigroup $(\mathbb{N},+)$ of the positive integers such that the set $\mathbb{N}\setminus A$ is finite. Equivalently (for a subsemigroup) ...
3
votes
1
answer
419
views
Relation on the set of connected components of the $\mathbb{C^*}$-fixed points locus coming from the Bialynicki-Birula decomposition
Let $X$ be a smooth variety with an action of $\mathbb{C}^*.$ One has the so-called Bialynicki-Birula decomposition of $X$ given by stable manifolds: $$X=\bigcup_N X^+(N),$$ where $N$ varies in the ...
user17778