Questions tagged [gn.general-topology]
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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Extending homeomorphisms on closure spaces
Let $C$ be an infinite $T_1$ closure space, which is not a topological space. Suppose $C$ has the exchange property: for $x,y\in C$ and $A\subseteq C$
$$
\big( x\notin\overline{A}, \hspace{4mm} x\in \...
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When can a generalized connected sum be aspherical
Let $M$ and $N$ be compact $n$-dimensional manifolds with a common (nicely embedded) compact submanifold $S$ (we may assume that the inclusion of $S$ in $M$ and $N$ is $\pi_1$-injective). Let $M\#_S N$...
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Density structure on Noetherian space
I'm confused about Example 2.23. in Voevodsky's Homotopy theory of simplicial sheaves in completely decomposable topologies
I'm considering this example: over an algebraically closed field $k$, let $...
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Extensions of bounded uniformly continuous functions
Let $X$ be a uniform space, $S\subseteq X$ and $f:S\to \mathbb{R}$ bounded uniformly continuous, then there exists a uniformly continuous extension of $f$ to $X$. (Katětov, 1951)
I am looking for ...
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The topological entropy of potential space filling curves on the unit interval
By a potential space filling curve we mean a continuous function $f:[0,1]\to [0,1]$ such that there is a continuous surgective function $g:[0,1]\to [0,1]^2$ with $f=\pi_1 \circ g$ where $\pi_1$...
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Consistency of the Rothberger property [closed]
Are there any models with this property present? With large cardinals? I am having trouble finding it though there's papers showing that its equivalent to other notions.
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When can we extend a diffeomorphism from a surface to its neighborhood as identity?
Let $M$ be a closed and simply-connected 4-manifold and let $f: M^4 \to M^4$ be a diffeomorphism such that $f^*: H^*(M;\mathbb{Z})\to H^*(M;\mathbb{Z})$ is the identity map. Moreover, let $\Sigma \...
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The analogy between dualizable categories and compact Hausdorff spaces
Efimov has in his recent preprint K-theory and localizing invariants of large categories, Appendix F, a long table of analogies between the categories $\text{Cat}^\text{dual}_\text{st}$ and $\text{...
- 2,213
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Well-embedded type property for bounded functions
According to @Tyrone the term well-embedded set was first used in Measures on Metacompact Spaces by W. Moran.
In the article Extensions of Zero-sets and of Real-valued Functions by R. Blair and A. ...
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Sheaf cohomology of non-paracompact manifolds (e.g. the long line)
I have long heard that manifolds are "affine". If we allow non-paracompact manifolds, then this seems to fail, since as explained in Dmitri Pavlov's answer, the Serre–Swan theorem fails. I ...
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Does there exist a Dehn filling of an irreducible 3-manifold with toroidal boundaries which is still irreducible?
Let $M$ be a compact, orientable, irreducible 3-manifold with incompressible toroidal boundary (there might be more than one boundary component). Is it always possible to choose appropriate slopes on ...
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A question regarding weak Whitney embedding theorem
The weak Whitney embedding theorem states that any continuous map $f: D^n \to \mathbb{R}^{2n+1}$ (Let us focus on $D^n$ for this question) can be approximated (in $C^0$-norm) by embeddings. A counter ...
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"Locally compact"-ly generated topological spaces
Let $P$ be a property of topological spaces - here I am interested in "compact" and "locally compact".
A topological space $X$ is $P$-ly-generated if, for any topological space $Y$,...
user531303
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Injective envelope of B(H)
$B(\ell^2)$ is an injective operator system by a result of Arveson. However, $B(\ell^2)$ is not an injective Banach space, since it is not linearly isomorphic to a $C(K)$ space (for instance, $C(K)$ ...
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Is there a metric compactification that doesn't create new paths?
Every separable metric space $A$ has a metrizable compactification, i.e. a compact metrizable space $X$ for which $A$ embeds topologically as a dense subspace of $X$. There are many approaches to ...
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