Question

Doubt about open sets in the Product topology

score 154 · Answer 1 · 2019-10-20 10:02:22

154

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Doubt about open sets in the Product topology

Published on 20 Oct 2019 - 10:02

score 47 · Answer 2 · 2019-11-01 20:11:57

47

Views

Show that $ \ g_2: \Bbb R \to \Bbb R$ given by $g_2: x \to x^{-1}$ (inverse map) is not continuous.

Published on 01 Nov 2019 - 20:11

score 181 · Answer 3 · 2026-03-22 17:05:03

181

Views

A converse version of Fubini's Theorem

Published on 22 Mar 2026 - 17:05

score 338 · Answer 4 · 2019-11-15 21:17:56

338

Views

Can $\mathbb{R}^2$ be homeomorphic to $\mathbb{R}\times\mathbb{R}$ with this topology?

Published on 15 Nov 2019 - 21:17

score 165 · Answer 5 · 2026-02-23 02:54:35

165

Views

Why is $2^{\mathbb{N}}$ Homeomorphic to $2^{\mathbb{N}^{< \mathbb{N}}}$?

Published on 23 Feb 2026 - 2:54

score 211 · Answer 6 · 2026-02-23 02:48:21

211

Views

$\Bbb R^J$ is a Baire space in product topology

Published on 23 Feb 2026 - 2:48

score 89 · Answer 7 · 2019-11-28 14:47:18

89

Views

$f\times\text{id}$ is closed for a closed map $f$ with $f^{-1}(y)$ compact $\forall y\in Y$

Published on 28 Nov 2019 - 14:47

score 43 · Answer 8 · 2019-12-03 20:50:55

43

Views

Visualizing: "Altering a finite set of coordinates cannot change the value of a continuous function $f:X \to \{0,1\}$"

Published on 03 Dec 2019 - 20:50

score 96 · Answer 9 · 2019-12-05 14:11:33

96

Views

$A$ is homeomorphic to $A\times A$

Published on 05 Dec 2019 - 14:11

score 597 · Answer 10 · 2019-12-23 20:32:06

597

Views

A sequence with no converging subsequence that clusters everywhere

Published on 23 Dec 2019 - 20:32

score 645 · Answer 11 · 2019-12-24 21:05:58

645

Views

Is the Product of a Compact Space and a Countably Compact Space Countably Compact?

Published on 24 Dec 2019 - 21:05

score 339 · Answer 12 · 2019-12-26 22:06:48

339

Views

Are $(0,1) \times [0,1)$ and $[0,1) \times [0,1)$ homeomorphic?

Published on 26 Dec 2019 - 22:06

score 347 · Answer 13 · 2019-12-27 17:20:24

347

Views

Homeomorphism to graph

Published on 27 Dec 2019 - 17:20

score 48 · Answer 14 · 2019-12-30 16:23:46

48

Views

Example Problem from "Lecture Notes on Elementary Topology and Differential Geometry" (Singer/Thorpe)

Published on 30 Dec 2019 - 16:23

score 362 · Answer 15 · 2019-12-31 13:11:54

362

Views

Topological space which is homeomorphic to its square

Published on 31 Dec 2019 - 13:11

List Question

Doubt about open sets in the Product topology

Show that $ \ g_2: \Bbb R \to \Bbb R$ given by $g_2: x \to x^{-1}$ (inverse map) is not continuous.

A converse version of Fubini's Theorem

Can $\mathbb{R}^2$ be homeomorphic to $\mathbb{R}\times\mathbb{R}$ with this topology?

Why is $2^{\mathbb{N}}$ Homeomorphic to $2^{\mathbb{N}^{< \mathbb{N}}}$?

$\Bbb R^J$ is a Baire space in product topology

$f\times\text{id}$ is closed for a closed map $f$ with $f^{-1}(y)$ compact $\forall y\in Y$

Visualizing: "Altering a finite set of coordinates cannot change the value of a continuous function $f:X \to \{0,1\}$"

$A$ is homeomorphic to $A\times A$

A sequence with no converging subsequence that clusters everywhere

Is the Product of a Compact Space and a Countably Compact Space Countably Compact?

Are $(0,1) \times [0,1)$ and $[0,1) \times [0,1)$ homeomorphic?

Homeomorphism to graph

Example Problem from "Lecture Notes on Elementary Topology and Differential Geometry" (Singer/Thorpe)

Topological space which is homeomorphic to its square

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