All Questions
5,184 questions
4
votes
3
answers
213
views
Cancellation of contractibility of fibres
Suppose given maps $f:X \to Y$ and $g:Y \to Z$ such that $f$ and $g \circ f$ both have contractible fibres. Then does $g$ have contractible fibres?
And, the same question, but with the maps assumed ...
- 8,723
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
2
votes
2
answers
2k
views
Maximum number of shortest-paths
I would like to know if there is a equation for the maximum number of shortest paths that pass through r where r is a node contained in any path from node s (a fixed node, i mean, s is the only source ...
- 23
1
vote
0
answers
99
views
Set nor its compliment contain an uncountable closed set [closed]
Does there exist a set $X$ subset of the real numbers such that no uncountable closed set is contained in $X$ or $X^c$?
- 121
0
votes
1
answer
232
views
Kernel elements for the Grothendieck group map of a commutative monoid
This is just a nomenclature question. Let $T$ be a commutative monoid, and let $T^*$ be its Grothendieck group. That is, $T^* \cong T \times T \ / \sim$, where $(s,s') \sim (t, t')$ if $s+t'+e = s'+t+...
- 8,512
1
vote
0
answers
143
views
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
8
votes
1
answer
621
views
Sober except not $T_0$?
tl;dr: Is there an accepted or proposed term for a topological space whose $T_0$ quotient is sober?
The condition that a topological space be sober (and therefore equivalent to a locale) may be ...
- 2,754
5
votes
0
answers
137
views
Pseudovarieties of monoids
All (pseudo)varieties considered here are (pseudo)varieties of monoids.
It is known that any (finite or infinite) monoid that satisfies the identities
\begin{equation}
xhxyty = xhyxty, \quad xhytxy=...
- 563
4
votes
0
answers
77
views
Catenarity of monoid algebras
Let $R$ be a commutative ring, let $M$ be a commutative monoid, and let $R[M]$ denote the corresponding monoid algebra. Suppose further that $R$ is universally catenary. One may ask for conditions on $...
- 6,700
0
votes
2
answers
259
views
Can we generalize the result of Urysohn's lemma to countable collection of pairwise disjoint closed subsets of a normal space..?
Suppose X is a normal topological space. Suppose some metric space for example.
If {$A_n$}$_{n=1}^{\infty}$ is a collection of pairwise disjoint closed subsets of X, can we find a continuous function ...
- 111
1
vote
1
answer
190
views
Is the semigroup M(n, Z) finitely presented? If so, where can I find a presentation of it?
I am new to semigroup research, so I apologize if this is an easy question.
- 87
5
votes
1
answer
296
views
Solenoid of a continuous map of a ball, is it contractible?
Let $B$ be the closed unit ball in $\mathbb R^n$ and $f\colon B\to B$ a continuous map.
Consider the infinite product $B^{\mathbb Z}$ equipped with the product topology. Consider the solenoid
$$
S_f=\...
- 4,188
3
votes
0
answers
141
views
Non-finitely based varieties and pseudovarieties
The variety of semigroups defined by $B=\Big\{(x^py^p)^2=(y^px^p)^2:p \text{ is prime}\Big\}$ is non-finitely based (Isbell, 1970). Is the pseudovariety defined by $B$ also non-finitely based?
More ...
- 563
3
votes
0
answers
126
views
dual composition of binary relations
I'm not sure if this is of any interest at all, but I spent some time looking at it a couple of years ago so I'd like to ask for input on this.
Given two binary relations $\rho,\,\sigma$ on a set $X,$...
- 1,445
3
votes
0
answers
122
views
A topological space extracting from a group action
Let $G$ be a compact abelian topological group with invariant measure $\mu$ which acts on a compact Hausdorff space $X$. A $G$-odd function is a continuous function $f:X\to \mathbb{C}$...
- 356
2
votes
1
answer
413
views
Technique: Compactness => (Finite -> Reals)
Context
I'm studying a classical results of Erdos and Lovasz, on colorings of the real line.
The theorem to be proved is as follows:
Let $m, k$ be two positive integers satisfying:
$$e(m(m-1)+1)k\...
- 23
0
votes
2
answers
212
views
Is there a normal space that is not uniformly normal
Let $(X,\mathcal D)$ be a uniform space and $A,B\subseteq X$. Let's say $A$ is uniformly inside $B$ and write $A\le B$ iff there's some entourage $D$ for which
$$(\forall a\in A)(D[a]\subseteq B)$$
A ...
user31967
2
votes
1
answer
236
views
Does every proximal outer measure, measure all open sets?
Let $\: \langle X,\delta\rangle \: $ be a separated proximity space.
Let $\: \mu^* \: : \: 2^{X} \: \to \: [0,+\infty] \: $ be a proximal outer measure.
Let $U$ be an open subset of $X$.
Does it ...
user5810
3
votes
2
answers
447
views
Number of non-intersecting non-homotopic simple closed curve
How many simple closed curves can be put on a orientable genus $g$ surface $\Sigma_g$ such that the following are true:
The curves are pairwise non-homotopic
The curves are pairwise set-theoretically ...
user13946
0
votes
1
answer
277
views
Diffeomorphisms of a surface in terms of generators.
I am interesting in a presentation of a diffeomorphisms in terms of generators. Is it possible to obtain such presentation in some cases, depending on a genus of a surface or a type of diffeomorphism (...
- 192
3
votes
1
answer
589
views
Extending open maps to Stone-Cech compactifications
(Cross posted from this math.SE question)
Let $X$ be a Cech-complete space, and $Y$ a paracompact space. Suppose $f\colon X\to Y$ is a continuous and open surjection.
Since $Y$ is completely ...
- 39.8k
2
votes
1
answer
727
views
pseudo-Anosov maps on surfaces with boundary
In "Automorphisms of Surfaces after Nielsen & Thurston" by Casson & Bleiler (on pages 75 - 80) they discuss classifying automorphisms of a surface. They show that, if $S$ is a closed ...
- 3,165
2
votes
1
answer
457
views
About subspaces of $F$-spaces
A topological space $X$ is an $F$-space, if Every finitely generated ideal in the ring of all continuous functions on $X$,denoted by $C(X)$, is principal. The text "Rings of continuous functions" ...
- 1,788
-2
votes
2
answers
954
views
Three modifications of connectedness
This question arose in my research of generalized connectedness (see this draft article for the overall idea, but beware that the draft is yet too preliminary and unreadable, however I hope you can ...
2
votes
1
answer
153
views
How to visulize surface link in four dimension?
I am now facing a problem with "surface link" in four dimension. I have heard that three 2-torus can be linked in four dimension. And I have created a movie by cutting four dimensional space with ...
- 293
0
votes
2
answers
643
views
Collinear vertices and definition of k-simplex
On page 120 of his Basic Topology, Armstrong defines the $k$-simplex in $\mathbb{E}^n$ with verices $v_0,\ldots,v_k$ to be complex hull of said vertices. (A similar definition is given on Wikipedia).
...
- 3,079
1
vote
3
answers
884
views
Does the manifold of the three dimensional group of rotations SO(3) cause a separation of space in the group of rigid motions SE(3)?
The group of three dimensional rotations $SO(3)$ is a subgroup of the Special Euclidean Group $SE(3) = \mathbb{R}^3 \rtimes SO(3)$. The manifold of $SO(3)$ is the three dimensional real projective ...
- 13
2
votes
1
answer
177
views
Syndetically separated topological groups
I am looking for examples for a certain kind of topological groups:
Definition: A topological group G is called syndetically separated if for every compact subset $K \subseteq G \setminus \{1\}$ ...
- 1,498
2
votes
2
answers
300
views
what conditions can one place on a finitely generated periodic semigroup that will ensure the semigroup is finite?
I am not familiar with much semigroup theory, but this question came up in my research and I've been unable to find much on it.
- 549
3
votes
1
answer
695
views
Hausdorff-dimension of connected closed subsets of R^2
Let $A \subseteq \mathbb{R}^2$ be closed and connected, and for any $c \in \mathbb{R}$, let $A_c \subseteq A$ be a closed and connected subset of $A$, s.t. for $c \neq d$ we have $A_c \cap A_d = \...
- 4,727
4
votes
1
answer
490
views
A question on PL-topology and polytopal complex
Question : $C$ is a pure, full-dimensional polytopal complex(a special case of a regular cell complex) in $\mathbb{R}^d$. I know that the boundary of the underlying set is a PL-sphere. Is it true that ...
- 113
0
votes
1
answer
208
views
The pth power of a distance function is twice continuously differentiable, for $p>2$?
Suppose $\mathcal{O}$ is an open convex connected strict subset in $\mathbb{R}^n$ and define $\beta(x)=dist(x, \mathcal{O})$, for each $x\in\mathbb{R}^n$.
Is $\beta^p$, $p>2$ a twice continuously ...
- 9
3
votes
0
answers
115
views
Characterization of global sections (which are not products) of a sheaf which is locally a product
In order to compute certain group cohomology sets I have come upon a construction which seems rather general concerning sheaves which are locally products. So I will state the problem here in a ...
- 397
0
votes
2
answers
641
views
Looking for general approaches to show connectedness of topological groups
Let $G$ be a topological group. One general approach to show that $G$ is connected is the following:
For every subgroup $H\leq G$ (not necessarily closed) we have a projection map:
$$
\pi: G\...
- 7,609
9
votes
0
answers
102
views
A 2 dimensional Sharkovskii type Theorem
Does there exist a homeomorphism of $\mathbb{R}^2$ with a periodic point of period three and no fixed points? Note that according to a theorem from Brouwer such homeomorphism must be orientation ...
- 615
1
vote
0
answers
226
views
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
0
votes
1
answer
305
views
Embedding a semigroup into a divisible semigroup
The following is motivated by the fact that I'd like to have a way, much better if canonical, to isometrically embed a normed group into a normed divisible group. But semigroups are a much more ...
- 10.5k
5
votes
0
answers
179
views
Is the space of $C^r$ vector fields inducing locally uniformly bounded trajectories Baire?
Let $\mathcal{V}$ be the space $C^r$ vector fields on a non-compact (smooth) manifold $M$. Being a subspace of $C^r(M, T M)$, it inherits the natural $C^r$ topology (i.e. the strong topology) of that ...
1
vote
1
answer
716
views
An example of a space which is locally relatively contractible but not contractible?
A space $X$ is called locally contractible it it has a basis of neighbourhoods which are themselves contractible spaces. CW complexes and manifolds are locally contractible. On the other hand, the ...
- 35.5k
3
votes
1
answer
129
views
perfect space without convergent long sequences
Is there a boolean space $X$ without isolated points with the property that no point $x\in X$ is the limit of a long sequence $(x_i)_{i\in I}$ from $X\setminus \lbrace x\rbrace $ ('long sequence' here ...
- 328
-1
votes
1
answer
416
views
the space of maximal ideals in C(X) and C*(X) [closed]
Let $C(X)$ be the continous function ring and $C*(X)$ be the bounded continous function ring.$Max C(X)$ consisting of all maximal ideals in $C(X)$.
Question:why $Max C(X)$ and $Max C*(X)$ are compact ...
- 21
1
vote
1
answer
133
views
Special finite subcover of a compact
Let $(a,b)\in \mathbb R^n$. We consider the following open cover of the compact line segment $[a,b]$: $$[a,b]\subset\underset{x\in [a,b]}{\bigcup}B(x,\rho_x),$$
where for $x\in K,B(x,\rho_x)$ is a ...
1
vote
1
answer
606
views
About deformation retract
Let $X\subset Y$ be CW-complexes. Denote $i\colon X\to Y$ be an inclusion map.
Is it true that $i$ is deformation retract if and only if $i$ is homotopy equivalence?
When I saw some papers about h-...
- 13
9
votes
1
answer
718
views
What is enough to conclude that something is a CW complex?
This question was something I considered when looking into CW-structures on Grassmannians, but I found no general treatment of this in the literature:
Question: Assume that $X$ is an $n-1$ ...
- 2,590
2
votes
2
answers
408
views
When a set of measure zero plus itself contains interior
Is there a characterization of measure zero subsets $A$ of $\mathbb R^n$, $n>1$ such that the set $A+A$ contains interior? Here $A+A$ is the set of points $\{ x+y \mid x, y\in A \}$.
Is it true ...
- 415
1
vote
0
answers
67
views
Extending an homotopy, knowing the two base functions extend
Let $A\subset B$ be paracompact spaces, and let $C$ be a paracompact space.
Let $f_0,f_1:A\rightarrow C$ be continuous functions. $F:A\times[0,1]\rightarrow C$ a homotopy from $f_0$ to $f_1$. Suppose ...
- 363
2
votes
0
answers
272
views
Continuity of multiplicative character
Let $G$ be a discrete group and $\beta (G)$ denote the Stone-Cech compactification of $G$, a right topological semigroup. By a multiplicative character, I mean a mapping that preserves multiplication ...
- 61
0
votes
1
answer
111
views
Is a weakly separable group always Lindelöf?
By "weakly separable" I mean the notion for uniform spaces used by David Wigner and Lawrence Brown: a uniform space is weakly separable if any uniform cover has a countable subcover. For a topological ...
- 135
2
votes
0
answers
104
views
Selecting dense diagonals in $\Bbb T^2$
Let $p$ be a prime number and let $G=\bigcup_{n\in \Bbb N}\{\exp(k\frac{2\pi i}{p^n})\mid k\in \Bbb Z\}$ be a Prüfer group. For homomorphisms $f,g:G\to G$ let $H_{f,g}=\{(f(x),g(x))\mid x\in G\}$. ...
- 1,145
3
votes
2
answers
392
views
Ring isomorphism $\Phi \colon C(X) \to C(Y)$ and zero dimensionality of $X$
We denote the ring of all continuous real-valued functions on $X$ by $C(X)$. The ring of all bounded continuous real valued functions on $X$ is denoted by $C_b(X)$. One of the goals of the study of $...
- 1,788