Question

How can a closed set in a finer topology be closed in a coarser topology?

score 221 · Answer 1 · 2022-08-10 12:41:37

221

Views

How can a closed set in a finer topology be closed in a coarser topology?

Published on 10 Aug 2022 - 12:41

score 170 · Answer 2 · 2022-08-15 13:13:16

170

Views

Under what conditions does a non measurable dense set necessarily intersect every closed uncountable set?

Published on 15 Aug 2022 - 13:13

score 89 · Answer 3 · 2022-08-23 17:19:59

89

Views

axiom of choice and existence of non-smooth Borel equivalence relation

Published on 23 Aug 2022 - 17:19

score 188 · Answer 4 · 2022-08-23 22:02:43

188

Views

a non-Borel equivalence relation whose every equivalence class is Borel

Published on 23 Aug 2022 - 22:02

score 68 · Answer 5 · 2026-02-23 12:07:51

68

Views

Examples of dense and codense $G_\delta$ subsets of $\mathbb{R}^2$ that are not homeomorphic to $\mathcal{N}=\mathbb{N}^\mathbb{N}$

Published on 23 Feb 2026 - 12:07

score 343 · Answer 6 · 2022-09-02 01:17:16

343

Views

Prove that the set of condensation points is closed

Published on 02 Sep 2022 - 1:17

score 202 · Answer 7 · 2022-09-04 02:39:02

202

Views

Continuum hypothesis analogue for substructures

Published on 04 Sep 2022 - 2:39

score 47 · Answer 8 · 2022-09-04 04:23:19

47

Views

What are some interesting implications of this similarity?

Published on 04 Sep 2022 - 4:23

score 96 · Answer 9 · 2026-02-23 13:30:20

96

Views

Is this cardinal characteristic trivial? (Number of strategies needed to guarantee at least one win)

Published on 23 Feb 2026 - 13:30

score 71 · Answer 10 · 2026-02-23 12:07:51

71

Views

Is Homeo$(X)$ a $G_\delta$ subset of $C(X,X)$?

Published on 23 Feb 2026 - 12:07

score 75 · Answer 11 · 2022-09-07 09:52:24

75

Views

In what kind of Polish spaces is there a subset without the Baire property?

Published on 07 Sep 2022 - 9:52

score 63 · Answer 12 · 2022-09-19 20:55:17

63

Views

Every polish space $X$ has a total ordering that is polish as a subset of $X^2$

Published on 19 Sep 2022 - 20:55

score 159 · Answer 13 · 2022-09-22 21:18:37

159

Views

What is the Lebesgue measure of Luzin's non-Borel set of reals?

Published on 22 Sep 2022 - 21:18

score 72 · Answer 14 · 2022-10-02 13:46:25

72

Views

Existence of Perfect subset for any given measure

Published on 02 Oct 2022 - 13:46

score 164 · Answer 15 · 2022-10-10 12:04:57

164

Views

Proving that the set of points where a continuous function is differentiable is a $\mathbf{\Pi_3^0}$ set

Published on 10 Oct 2022 - 12:04

List Question

How can a closed set in a finer topology be closed in a coarser topology?

Under what conditions does a non measurable dense set necessarily intersect every closed uncountable set?

axiom of choice and existence of non-smooth Borel equivalence relation

a non-Borel equivalence relation whose every equivalence class is Borel

Examples of dense and codense $G_\delta$ subsets of $\mathbb{R}^2$ that are not homeomorphic to $\mathcal{N}=\mathbb{N}^\mathbb{N}$

Prove that the set of condensation points is closed

Continuum hypothesis analogue for substructures

What are some interesting implications of this similarity?

Is this cardinal characteristic trivial? (Number of strategies needed to guarantee at least one win)

Is Homeo$(X)$ a $G_\delta$ subset of $C(X,X)$?

In what kind of Polish spaces is there a subset without the Baire property?

Every polish space $X$ has a total ordering that is polish as a subset of $X^2$

What is the Lebesgue measure of Luzin's non-Borel set of reals?

Existence of Perfect subset for any given measure

Proving that the set of points where a continuous function is differentiable is a $\mathbf{\Pi_3^0}$ set

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