User Taras Banakh

46 votes

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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

29 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

22 votes

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Is the Golomb countable connected space topologically rigid?

answered Nov 12, 2017 at 15:24

21 votes

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"Anti" fixed point property

answered Nov 11, 2017 at 10:23

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

16 votes

Examples of common false beliefs in mathematics

answered Feb 27, 2018 at 11:27

16 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

16 votes

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

answered Nov 24, 2022 at 6:53

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

answered Nov 23, 2017 at 10:05

14 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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A ridiculous combinatorial cardinal characteristic of the continuum?

answered Nov 9, 2018 at 18:30

13 votes

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Is every second-countable Hausdorff space symmetrizable?

answered May 30, 2022 at 18:40

13 votes

Is every connected subgroup of a Euclidean space closed?

answered Oct 4 at 14:02

12 votes

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Example of an uncountable scattered space with some properties

answered Feb 17, 2022 at 20:51

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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Analogue of Urysohn metrization for Lawvere metric spaces?

answered Sep 1, 2018 at 6:47

12 votes

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Is a Borel image of a Polish space analytic?

answered Jan 11, 2019 at 11:27

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

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300 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 $X,Y$?

Is the Golomb countable connected space topologically rigid?

"Anti" fixed point property

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?

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

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 $\text{Cont}(\mathbb{R},\mathbb{R})$ 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?

A ridiculous combinatorial cardinal characteristic of the continuum?

Is every second-countable Hausdorff space symmetrizable?

Is every connected subgroup of a Euclidean space closed?

Example of an uncountable scattered space with some properties

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

Analogue of Urysohn metrization for Lawvere metric spaces?

Is a Borel image of a Polish space analytic?

Extension of Baire's Theorem

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