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https://math.stackexchange.com/questions/5133668/can-the-definition-of-a-t1-space-be-simplified
general topology - Can the definition of a T1 space be simplified? - Mathematics Stack Exchange
There are a number of equivalent definitions of a $T_1$ space, circling around the concept that: every singleton is a closed set for every pair of points, each...
mathematics stack exchangegeneral topologydefinitiont1space
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General Topology
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https://mathoverflow.net/questions/243639/finitely-additive-measures-on-boolean-algebras-of-regular-open-subsets-is-there
gn.general topology - Finitely additive measures on Boolean algebras of regular open subsets: Is...
Let $\mathcal{X}$ be a topological space. An open subset $\mathcal{R}\subseteq\mathcal{X}$ is regular if it is the interior of its own closure. The...
gn general topologyadditivemeasuresbooleanalgebras
https://math.stackexchange.com/questions/5134606/showing-that-there-is-no-immediate-deformation-retraction-to-a-point
general topology - Showing that there is no immediate deformation retraction to a point -...
Let $$X = \overline{B}_{n + 1},$$ $$C = \{x \in X: (\forall i \in (n + 1) \setminus \{0\}: x_i = 0) \land x_0 \geq 0\},$$ $$A = S_n \cup C,$$ where...
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https://mathoverflow.net/questions/510544/straightening-a-polygonal-arc-in-the-plane
gn.general topology - Straightening a Polygonal Arc in the Plane - MathOverflow
In preparation for a book, a friend and I are trying to cheat our way to the Schoenflies Theorem in $\mathbb{R}^2$ and we have a reduction which seems very...
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https://mathoverflow.net/questions/510590/who-coined-the-term-clopen
gn.general topology - Who coined the term "clopen"? - MathOverflow
I was not sure whether this question is appropriate for this forum, but a quick search suggests that there is at least some precedent for asking about the...
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https://www.cambridge.org/highereducation/books/general-topology-for-beginners/3BD5141C1821C6CF3A78BB2ECDC937D3
General Topology for Beginners | Cambridge Aspire website
Discover General Topology for Beginners, 1st Edition, Jay Mehta on Cambridge Aspire website
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https://mathoverflow.net/questions/510590/who-coined-the-term-clopen?noredirect=1
gn.general topology - Who coined the term "clopen"? - MathOverflow
I was not sure whether this question is appropriate for this forum, but a quick search suggests that there is at least some precedent for asking about the...
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https://mathoverflow.net/questions/509712/non-constant-maps-between-t-2-spaces
gn.general topology - Non-constant maps between $T_2$-spaces - MathOverflow
Are there $T_2$-spaces $X, Y$, each having more than $1$ point, such that every continuous map $f:X\to Y$ is constant, and every continuous map $g:Y\to X$ is...
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https://mathoverflow.net/questions/509638/isotopy-to-achieve-finite-intersections
gn.general topology - Isotopy to achieve finite intersections - MathOverflow
I've asked this question on math.stackexchange a week ago, with no response. More context is available there. Suppose that $\alpha$ and $\beta$ are closed...
gn general topologyachievefiniteintersectionsmathoverflow
https://mathoverflow.net/questions/504760/a-property-which-combines-total-paracompactness-and-strong-paracompactness
gn.general topology - A property which combines total paracompactness and strong paracompactness -...
Def 1. We call $X$ strongly paracompact if every open cover has a star-finite open refinement. Def 2. We call $X$ paracompact if every open cover has locally...
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https://mathoverflow.net/questions/509206/is-the-complement-of-the-support-of-a-measure-on-a-topological-space-a-set-of-me
gn.general topology - Is the complement of the support of a measure on a topological space a set of...
$\DeclareMathOperator{\supp}{supp}$ Let $\mu$ be a (Borel) measure on a topological space $(X,T)$. By definition, for any $x \in \supp(\mu)^c$, it exists an...
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https://mathoverflow.net/questions/510532/topological-version-of-arzela-ascoli-theorem
gn.general topology - Topological version of Arzela-Ascoli theorem? - MathOverflow
Equip $C(X, Y)$ with compact-open topology. Theorem. (Arzela-Ascoli) If $X, Y$ are Hausdorff and $Y$ is a uniform space, $S\subseteq C(X, Y)$ is pointwise...
gn general topologytopologicalversionascolitheorem
https://mathoverflow.net/questions/510052/is-the-countable-box-product-of-real-lines-a-%c4%8cech-complete-space
gn.general topology - Is the countable box product of real lines a Čech-complete space? -...
This answer by Henno Brandsma points to this article by Frolik, where it's shown that countable box products of countably complete spaces are countably...
gn general topologybox productcountablereallines