All Questions
5,184 questions
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Shrinking Group Actions
This is a repost from stackexchange. I didn't get an answer, so I figured I'd ask it here.
Suppose $H\subset G$ is a subgroup of a topological group $G$, and $Y\subset X$ is a subspace of a ...
- 2,751
5
votes
0
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336
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Defining a topology by means of closed subsets in a topos
In the following we fix a topos. I'll speak of sets instead of objects and of subsets instead of subobjects.
Let $X$ be a set and assume $F$ is a set of subsets of $X$ that contains $\emptyset, X$, ...
- 63.1k
0
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179
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semigroup actions of groups on regular rooted trees
If $G$ is a group which has a semigroup action on a regular rooted tree via prefix-preserving, continuous transformations (I give the tree the path metric), what kinds of algebraic restrictions can we ...
- 125
3
votes
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answers
294
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Monomorphisms in geometry
What is known about monomorphisms in the following categories:
Schemes
Complex manifolds
$C^\infty$--manifolds
and any other kinds of geometric objects that you might think of.
How do we choose a ...
- 123
1
vote
0
answers
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 $\theta:(x_0,\ldots,x_N)\to (-x_0,\ldots,-x_N)$;
$({\...
5
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0
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135
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Possible homogeneity of infinite dimensional Sierpinski carpet analogues?
Start with the Hilbert cube $H=I^\omega$, thinking of its coordinates as written in ternary expansion.
Construct subsets $S_n$ by removing points from $H$ if for any $m$,
at least $n$ of the ...
- 17.6k
2
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0
answers
203
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Faithful actions of finite groups on topological spaces
Suppose that $G$ is a finite group acting faithfully on a topological space $X$. In the smooth setting, one can deduce that for each $x$ in $M$, the induced map $$G_x \to Diff_x\left(M\right)$$ from ...
- 15.5k
-3
votes
2
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314
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Dispensing with the notion of infinity for the sake of coverings [closed]
Instead of taking a one to one correspondence meaning each set has the same number of elements. why not use the concept of coverings of topology? The irrational numbers covers the whole numbers but ...
- 117
2
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0
answers
121
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Graphs, non-Hausdorfness and Wallman compactifications of non-regular spaces
Given a non-Hausdorff space $X$, one can form a graph $G_X$: vertices the points of $X$, edges indicating point pairs not separated by open sets. Up to graph-theoretically (but not topologically) ...
- 17.6k
2
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0
answers
199
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Finite topological dimension x local compactness
Of course, the two notions are independent one from the other, but often one of them implies the other under some additional hypotheses. For instance:
A topological vector space is finite dimensional ...
- 4,729
8
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302
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In a locally contractible space can we find local bases of contractible sets whose closures are locally contractible?
In a locally contractible topological space $X$ is it possible at each point $x$ to find a local basis of contractible sets $U_i\ni x$ such that the closure of each set $\overline{U_i} \subset X$ is ...
5
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350
views
Chain/Hierarchy of Monoids
Let's assume that we have the following collection of structures:
Some space $P$.
Monoids $(M_{i+1},\circ_{i+1})$, and
Actions $\bullet_{i+1}:M_{i+1}\times M_i\to M_i$, for $i\ge 0$
And $\bullet_{0}:...
- 1,882
2
votes
0
answers
299
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Uniqueness of dimension for topological vector spaces
Let $V$ be a complete Hausdorff locally convex topological vector space over the field $\mathbb{K}$.
Let $B$ be a subset of $V$ satisfying
.
Linearly Independent: For all functions $f$ in $\mathbb{...
user5810
0
votes
1
answer
194
views
Difference between a partial selector and a selector...
In Kharazishvili's "Nonmeasurable Sets and Functions" there is the following theorem:
There exists a subset $X$ of $\mathbb{R}$ which is a Vitali set and a Bernstein set.
The proof is as follows:
...
- 463
0
votes
0
answers
189
views
On Birman-Wenzlyfying the B2 spider
Prelude: First of all, let "S matrix" denote "an abstract 4D tensor satisfying
the usual isotypy rules (with no arrows!)". I'm busy trying to classify all possible
S matrices (paper pending) - it's ...
- 4,829
0
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1
answer
137
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Connectedness of a union regading a proximity
Let δ is a proximity.
I will call a set A connected iff for every partition {X,Y} of the set A holds X δ Y.
Question: Let A and B are sets with non-empty intersection. Let both A and B ...
- 765
1
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0
answers
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
4
votes
0
answers
137
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Does this property of scattered spaces have a name?
(Note: I asked this question at MSE a week ago and received no answer, so I am now reposting it here.)
Let $K$ be a (Hausdorff) scattered topological space and for each ordinal $\alpha$ denote by $K^{...
- 2,378
0
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1
answer
147
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Small set of acts over a countable monoid?
Given a countable monoid $S$, is the set of all (isomorphic representatives of) $S$-acts a small set?
- 11
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2
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172
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small extensions of the free semigroup of rank 1
Let N denote the free semigroup of rank 1. Say that a semigroup T is a small extension
of N if N embeds in T and |T - N| is finite. Is there some kind of classification
of small extensions of N? ...
- 91
1
vote
1
answer
154
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undecidability in the dynamics of functions $f: \Sigma^* \rightarrow \Sigma^*$
Does anyone know any undecidable problems in the dynamics of functions (not necessarily monoid homomorphisms or anything) from \Sigma^* to \Sigma^* where \Sigma is a finite set? In particular, I'm ...
- 549
1
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0
answers
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
4
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0
answers
296
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What is enough to conclude that something is a CW complex (part II)?
A while ago I asked a question about recoqnizing CW complexes and got an extremely nice and concrete answer. However, I am still interested in a more general treatment of this and therefore pose the ...
- 2,590
1
vote
2
answers
193
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Something like Yoneda's lemma
This is inspired by The Whitehead for maps question.
Consider two maps f, g: X\to Y which happen to induce the same maps (of discrete spaces) ...
- 15.1k
3
votes
0
answers
267
views
Maps of loop spaces with infinity-bounded differential.
I am currently working with loop spaces of manifold and finite dimensional manifolds approximating these and the following comes up very naturally:
In the following piece-wise smooth means smooth on ...
- 2,590
1
vote
1
answer
107
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Approximate selection theorems for factoring through perfect maps
I have the following setup:
$X, Y$ are topological spaces (if it helps, they can both be $T_1$ and normal. They can even be countably paracompact. They can't be assumed paracompact). $V$ is a normed ...
- 1,331
2
votes
0
answers
270
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Homotopy equivalences and cores
Hi all,
Before asking my question, I need to fix some terms and notation.
Let $M$, $M'$ be locally compact, Hausdorff spaces, and $f:M\rightarrow M'$ a homotopy equivalence with homotopy inverse $g:...
- 93
3
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0
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168
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Mapping into Hurewicz cofibrations.
In Strøm's paper "The Homotopy Category is a Homotopy Category" he proves
(Lemma 4) that if $Y$ is compact and if $i:A\to X$ is a cofibration, then the induced map
$$
i_*: A^Y \to X^Y
$$
is also a ...
- 12.5k
2
votes
0
answers
185
views
Simple topological question on taking complements inside a simplex
We would like to know if the following claim is true:
(If you don't know the definition of a tropical hyperplane, then please consider the case when d=3)
Let $P_1,\cdots,P_d$ be full dimensional (...
- 113
2
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0
answers
223
views
Is the realization of a proper map of simplicial spaces proper ?
Let $f:X \rightarrow Y$ be a map of $m$-dimensional simplicial spaces (which means that all simplices above dimension $m$ are degenerate). Recall, that $f$ is a natural transformation of functors from ...
- 11.1k
2
votes
0
answers
123
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Constructing a lattice out of the set of metrics
Let $X$ be a space, and $d_1$ and $d_2$ be two metrics on $X$.
Define $S(x,y)= ${$\Sigma_2^l Min${$d_1(x_{k-1},x_k),d_2(x_{k-1},x_k)$}$:x_1=x, x_l=y, l finite $} $x$ and $y$ are two points in $X$
...
- 31
3
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0
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126
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More on continuous images of dense orders
In this question I asked if there was an analogue of connectedness which applied to dense orders which were not required to be complete. Between them, Noah and Joel showed that every (infinite) ...
- 3,612
2
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0
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77
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Characterizing local homeomorphisms into an exponent
Let $X$,$Y$, and $Z$ be (compactly generated) spaces. Suppose $f:Z \to Y^X$ is a local homeomorphism. How can we tell this from its adjoint $\tilde f:Z \times X \to Y$? I.e., I want a property $P$ ...
- 15.5k
0
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0
answers
62
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Order-convergence and interval topology on ${\cal P}(\omega)/(\text{fin})$
On any poset $(P, \leq)$ we can consider two different topologies that arise directly from the ordering relation.
1) Order convergence topolog $\tau_o(P)$ : By a set filter $\mathcal{F}$ on $P$ we ...
- 48.9k