Question

Doubt about open sets in the Product topology

score 157 · Answer 1 · 2026-04-12 14:10:25

157

Views

Doubt about open sets in the Product topology

Published on 12 Apr 2026 - 14:10

score 50 · Answer 2 · 2026-04-15 20:51:17

50

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 15 Apr 2026 - 20:51

score 182 · Answer 3 · 2026-05-10 18:04:13

182

Views

A converse version of Fubini's Theorem

Published on 10 May 2026 - 18:04

score 340 · Answer 4 · 2026-04-13 03:20:15

340

Views

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

Published on 13 Apr 2026 - 3:20

score 166 · Answer 5 · 2026-04-09 06:04:39

166

Views

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

Published on 09 Apr 2026 - 6:04

score 214 · Answer 6 · 2026-04-14 02:25:06

214

Views

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

Published on 14 Apr 2026 - 2:25

score 90 · Answer 7 · 2026-05-11 03:17:19

90

Views

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

Published on 11 May 2026 - 3:17

score 46 · Answer 8 · 2026-04-12 16:58:05

46

Views

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

Published on 12 Apr 2026 - 16:58

score 99 · Answer 9 · 2026-04-11 08:29:01

99

Views

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

Published on 11 Apr 2026 - 8:29

score 600 · Answer 10 · 2026-04-12 20:51:00

600

Views

A sequence with no converging subsequence that clusters everywhere

Published on 12 Apr 2026 - 20:51

score 648 · Answer 11 · 2026-04-10 23:15:14

648

Views

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

Published on 10 Apr 2026 - 23:15

score 342 · Answer 12 · 2026-04-11 08:40:57

342

Views

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

Published on 11 Apr 2026 - 8:40

score 351 · Answer 13 · 2026-05-11 00:30:43

351

Views

Homeomorphism to graph

Published on 11 May 2026 - 0:30

score 51 · Answer 14 · 2026-04-12 16:01:05

51

Views

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

Published on 12 Apr 2026 - 16:01

score 365 · Answer 15 · 2026-04-11 06:47:34

365

Views

Topological space which is homeomorphic to its square

Published on 11 Apr 2026 - 6:47

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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