User Taras Banakh

46 votes

Accepted

If $X$ and $Y$ are homotopy equivalent, then are $X \times \mathbb{R}^{\infty}$ and $Y \times \mathbb{R}^{\infty}$ homeomorphic?

answered Feb 20, 2018 at 6:43

32 votes

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Chromatic number of a topological space

answered Feb 5, 2018 at 16:52

28 votes

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Closed balls vs closure of open balls

answered Jun 28, 2018 at 10:09

28 votes

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Countable connected Hausdorff space

answered Nov 8, 2017 at 16:36

23 votes

Is $\mathbb{R}\cong\text{Cont}(X,Y)$ for some non-trivial spaces $X,Y$?

answered Jan 8, 2018 at 15:00

21 votes

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"Anti" fixed point property

answered Nov 11, 2017 at 10:23

21 votes

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Is the Golomb countable connected space topologically rigid?

answered Nov 12, 2017 at 15:24

20 votes

Does there exist a bijection of $\mathbb{R}^n$ to itself such that the forward map is connected but the inverse is not?

answered Sep 2, 2018 at 12:17

19 votes

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A parametric version of the Borsuk Ulam theorem

answered Jan 4, 2019 at 19:49

19 votes

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Does $\mathbb C\mathbb P^\infty$ have a group structure?

answered Feb 21, 2018 at 7:33

19 votes

A good place to read about uniform spaces

answered Aug 22, 2017 at 5:10

18 votes

Dividing a cake between $n-1$, $n$, or $n+1$ guests

answered May 5, 2019 at 11:34

17 votes

Is $\beta \mathbb{N}$ homeomorphic to its own square?

answered Jul 25, 2017 at 19:46

17 votes

Contractible topological groups

answered Aug 25, 2015 at 21:53

15 votes

Examples of common false beliefs in mathematics

answered Feb 27, 2018 at 11:27

15 votes

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Are Hausdorff measures on the real line Haar measures for some locally compact topology?

answered Feb 15, 2019 at 16:32

14 votes

Bijection $f: \mathbb R^n \to \mathbb R^n$ that maps connected onto connected sets must map closed connected onto closed connected sets?

answered Sep 6, 2018 at 5:36

14 votes

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Is the complement of a zero-dimensional subset of the plane path-connected?

answered Feb 3, 2020 at 5:35

14 votes

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

answered Nov 24, 2022 at 6:53

14 votes

Is $\text{Cont}(\mathbb{R},\mathbb{R})$ dense in $\mathbb{R}^\mathbb{R}$?

answered Nov 23, 2017 at 10:05

13 votes

What is the fewest number of points you must delete from $\mathbb{R}^3$ to make it not simply connected?

answered Sep 1, 2015 at 12:06

13 votes

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Is every second-countable Hausdorff space symmetrizable?

answered May 30, 2022 at 18:40

13 votes

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A ridiculous combinatorial cardinal characteristic of the continuum?

answered Nov 9, 2018 at 18:30

12 votes

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If $\text{dim}(X \times X) = 2\text{dim}(X)$, does $\text{dim}(X^n) = n\text{dim}(X)$?

answered Nov 23, 2018 at 4:51

12 votes

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Extension of Baire's Theorem

answered Nov 17, 2019 at 19:28

12 votes

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Surjective group homomorphism from $\text{Sym}(X)$ onto $\mathbb{Z}$

answered Apr 21, 2018 at 8:32

11 votes

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Does $[0,1]\cap \mathbb{Q}$ have a connected $T_2$ quotient?

answered Nov 12, 2017 at 15:37

11 votes

Rediscovery of lost mathematics

answered Feb 10, 2018 at 23:26

11 votes

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Analogue of Urysohn metrization for Lawvere metric spaces?

answered Sep 1, 2018 at 6:47

11 votes

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Is a Borel image of a Polish space analytic?

answered Jan 11, 2019 at 11:27

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298 Answers

If $X$ and $Y$ are homotopy equivalent, then are $X \times \mathbb{R}^{\infty}$ and $Y \times \mathbb{R}^{\infty}$ homeomorphic?

Chromatic number of a topological space

Closed balls vs closure of open balls

Countable connected Hausdorff space

Is $\mathbb{R}\cong\text{Cont}(X,Y)$ for some non-trivial spaces $X,Y$?

"Anti" fixed point property

Is the Golomb countable connected space topologically rigid?

Does there exist a bijection of $\mathbb{R}^n$ to itself such that the forward map is connected but the inverse is not?

A parametric version of the Borsuk Ulam theorem

Does $\mathbb C\mathbb P^\infty$ have a group structure?

A good place to read about uniform spaces

Dividing a cake between $n-1$, $n$, or $n+1$ guests

Is $\beta \mathbb{N}$ homeomorphic to its own square?

Contractible topological groups

Examples of common false beliefs in mathematics

Are Hausdorff measures on the real line Haar measures for some locally compact topology?

Bijection $f: \mathbb R^n \to \mathbb R^n$ that maps connected onto connected sets must map closed connected onto closed connected sets?

Is the complement of a zero-dimensional subset of the plane path-connected?

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

Is $\text{Cont}(\mathbb{R},\mathbb{R})$ dense in $\mathbb{R}^\mathbb{R}$?

What is the fewest number of points you must delete from $\mathbb{R}^3$ to make it not simply connected?

Is every second-countable Hausdorff space symmetrizable?

A ridiculous combinatorial cardinal characteristic of the continuum?

If $\text{dim}(X \times X) = 2\text{dim}(X)$, does $\text{dim}(X^n) = n\text{dim}(X)$?

Extension of Baire's Theorem

Surjective group homomorphism from $\text{Sym}(X)$ onto $\mathbb{Z}$

Does $[0,1]\cap \mathbb{Q}$ have a connected $T_2$ quotient?

Rediscovery of lost mathematics

Analogue of Urysohn metrization for Lawvere metric spaces?

Is a Borel image of a Polish space analytic?