User KP Hart

8 votes

When factors may be cancelled in homeomorphic products?

answered May 30, 2010 at 15:02

8 votes

Accepted

Is there a notion of a "perfectly regular" topological space?

answered Jun 22, 2010 at 14:13

8 votes

Accepted

Does countable compactness imply local compactness in Hausdorff spaces?

answered Aug 30, 2010 at 7:54

8 votes

Zero dimensional iff every closed set is a retract.

answered Jan 21, 2011 at 14:28

8 votes

Is there a set $S\subseteq [0,1]$ with $|S|=2^{\aleph_0}$ and distinct pairwise distances?

answered Oct 12, 2018 at 10:27

8 votes

Stone–Čech Compactification of $\mathbb{Z}$ with Fürstenberg Topology

answered Oct 23, 2018 at 13:29

8 votes

Accepted

Is the Euclidean topology on $\mathbb{R}$ contained in a maximal connected topology?

answered Nov 3, 2018 at 14:45

8 votes

Accepted

Can totally inhomogeneous sets of reals coexist with determinacy?

answered Jul 8, 2023 at 13:31

8 votes

Accepted

Is there an infinite topological space with only countably many continuous functions to itself?

answered Nov 9, 2022 at 22:11

8 votes

Implicit uses of Countable or Dependent Choice

answered Nov 10 at 17:35

8 votes

Accepted

Reference: If $X$ is metrizable, then $X$ is realcompact iff $|X|$ is non-measurable

answered Apr 20 at 15:36

8 votes

Accepted

Can $f: \mathbb{R}^2 \to \mathbb{R}$ be continuous, open and closed?

answered May 31 at 13:09

7 votes

Embeds in a topological W-group, or a W-space that embeds in a topological group?

answered Apr 7 at 20:09

7 votes

Accepted

On the equality $\{f\in C(X), f|_A=0\}+\{f\in C(X), f|_B=0\}=\{f\in C(X), f|_{A\cap B}=0\}$

answered Sep 12, 2022 at 21:20

7 votes

On the definition of a continuous function

answered Oct 21, 2022 at 8:22

7 votes

Accepted

Can any poset of cardinality $\leq 2^{\aleph_0}$ be embedded in ${\cal P}(\omega)/(\text{fin})$?

answered Aug 22, 2023 at 22:04

7 votes

Accepted

Continuous binary operations on $\beta\mathbb{N}$

answered Dec 16, 2018 at 12:02

7 votes

The Stone-Čech compactification of a inverse system

answered Jan 17, 2020 at 9:38

7 votes

Accepted

Sunflowers in maximal almost disjoint families

answered Jun 14, 2021 at 21:49

7 votes

Iterated forcing and CH

answered Jan 27, 2011 at 9:47

7 votes

How to construct a continuous finite additive measure on the natural numbers

answered May 9, 2012 at 11:12

7 votes

Accepted

Embedding ordinals with the order topology into connected $T_2$-spaces

answered Sep 20, 2018 at 20:15

6 votes

Are separability and ccc equivalent for closed subspaces of $\beta N$?

answered Sep 23, 2018 at 18:28

6 votes

Accepted

Sufficient conditions for a topological space to be regular $T_3$

answered Sep 27, 2018 at 9:53

6 votes

Accepted

Can the Boolean Algebra of regular open sets be isomorphic to ${\cal P}(\omega)/(\text{fin})$?

answered Sep 20, 2018 at 12:38

6 votes

Surjective order-preserving map $f:{\cal P}(X)\to \text{Part}(X)$

answered Oct 1, 2018 at 11:35

6 votes

Axiom of Choice and Vitali's theorem

answered May 18, 2012 at 18:52

6 votes

Accepted

Continuously selecting elements from unordered pairs

answered Oct 19, 2011 at 19:52

6 votes

A unique ultrafilter extending a union of filters?

answered Nov 25, 2011 at 14:27

6 votes

Examples of common false beliefs in mathematics

answered May 6, 2010 at 13:19

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213 Answers

When factors may be cancelled in homeomorphic products?

Is there a notion of a "perfectly regular" topological space?

Does countable compactness imply local compactness in Hausdorff spaces?

Zero dimensional iff every closed set is a retract.

Is there a set $S\subseteq [0,1]$ with $|S|=2^{\aleph_0}$ and distinct pairwise distances?

Stone–Čech Compactification of $\mathbb{Z}$ with Fürstenberg Topology

Is the Euclidean topology on $\mathbb{R}$ contained in a maximal connected topology?

Can totally inhomogeneous sets of reals coexist with determinacy?

Is there an infinite topological space with only countably many continuous functions to itself?

Implicit uses of Countable or Dependent Choice

Reference: If $X$ is metrizable, then $X$ is realcompact iff $|X|$ is non-measurable

Can $f: \mathbb{R}^2 \to \mathbb{R}$ be continuous, open and closed?

Embeds in a topological W-group, or a W-space that embeds in a topological group?

On the equality $\{f\in C(X), f|_A=0\}+\{f\in C(X), f|_B=0\}=\{f\in C(X), f|_{A\cap B}=0\}$

On the definition of a continuous function

Can any poset of cardinality $\leq 2^{\aleph_0}$ be embedded in ${\cal P}(\omega)/(\text{fin})$?

Continuous binary operations on $\beta\mathbb{N}$

The Stone-Čech compactification of a inverse system

Sunflowers in maximal almost disjoint families

Iterated forcing and CH

How to construct a continuous finite additive measure on the natural numbers

Embedding ordinals with the order topology into connected $T_2$-spaces

Are separability and ccc equivalent for closed subspaces of $\beta N$?

Sufficient conditions for a topological space to be regular $T_3$

Can the Boolean Algebra of regular open sets be isomorphic to ${\cal P}(\omega)/(\text{fin})$?

Surjective order-preserving map $f:{\cal P}(X)\to \text{Part}(X)$

Axiom of Choice and Vitali's theorem

Continuously selecting elements from unordered pairs

A unique ultrafilter extending a union of filters?

Examples of common false beliefs in mathematics