Question

Different ways to state the motivation of the definition of the product topology

score 864 · Answer 1 · 2026-03-26 09:34:16

864

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Different ways to state the motivation of the definition of the product topology

Published on 26 Mar 2026 - 9:34

score 990 · Answer 2 · 2017-08-19 07:42:02

990

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Sub basis for a product topology

Published on 19 Aug 2017 - 7:42

score 1.2k · Answer 3 · 2017-08-22 09:00:42

1.2k

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Is the product of two topological groups a topological group?

Published on 22 Aug 2017 - 9:00

score 577 · Answer 4 · 2017-08-24 02:57:40

577

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Product Spaces and Integrals of Indicator Functions

Published on 24 Aug 2017 - 2:57

score 111 · Answer 5 · 2017-08-26 20:19:33

111

Views

a base of some topology $T$ on $Z=X\times Y$

Published on 26 Aug 2017 - 20:19

score 59 · Answer 6 · 2017-09-01 16:19:17

59

Views

Each $X_\alpha$ is homeomorphic to a closed set in $\Pi_{\alpha \in A} X_\alpha$

Published on 01 Sep 2017 - 16:19

score 831 · Answer 7 · 2017-09-21 05:13:49

831

Views

(infinite) product of topological groups is topological group

Published on 21 Sep 2017 - 5:13

score 2k · Answer 8 · 2017-09-25 02:24:46

2k

Views

Cartesian product of open intervals is open (and of closed intervals is closed)

Published on 25 Sep 2017 - 2:24

score 498 · Answer 9 · 2017-09-30 21:04:46

498

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Prob. 8 (b), Sec. 20, in Munkres' TOPOLOGY, 2nd ed: All four topology on $\mathbb{R}^\infty$ are distinct

Published on 30 Sep 2017 - 21:04

score 170 · Answer 10 · 2017-10-01 09:22:11

170

Views

Prob. 3 (a), Sec. 21, in Munkres' TOPOLOGY, 2nd ed: A Finite Cartesian Product Of Metrizable Spaces Is Metrizable

Published on 01 Oct 2017 - 9:22

score 363 · Answer 11 · 2017-10-01 12:31:05

363

Views

Prob. 3 (b), Sec. 21, in Munkres' TOPOLOGY, 2nd ed: A Countably Infinite Cartesian Product Of Metrizable Spaces Is Metrizable

Published on 01 Oct 2017 - 12:31

score 338 · Answer 12 · 2017-10-05 02:30:19

338

Views

A product topology where we allow countably many open sets

Published on 05 Oct 2017 - 2:30

score 255 · Answer 13 · 2017-10-08 15:17:54

255

Views

If $X=\prod_{i \in I}X_i$ is regular, then $X_i$ is regular for every $i\in I$

Published on 08 Oct 2017 - 15:17

score 1.6k · Answer 14 · 2017-10-12 18:34:33

1.6k

Views

Prove that the product topology on $X \times Y$ need not be the co-finite topology.

Published on 12 Oct 2017 - 18:34

score 648 · Answer 15 · 2017-10-22 21:04:48

648

Views

Show that $X=\prod X_\alpha$ is path connected if and only if each $X_\alpha$ is path connected

Published on 22 Oct 2017 - 21:04

List Question

Different ways to state the motivation of the definition of the product topology

Sub basis for a product topology

Is the product of two topological groups a topological group?

Product Spaces and Integrals of Indicator Functions

a base of some topology $T$ on $Z=X\times Y$

Each $X_\alpha$ is homeomorphic to a closed set in $\Pi_{\alpha \in A} X_\alpha$

(infinite) product of topological groups is topological group

Cartesian product of open intervals is open (and of closed intervals is closed)

Prob. 8 (b), Sec. 20, in Munkres' TOPOLOGY, 2nd ed: All four topology on $\mathbb{R}^\infty$ are distinct

Prob. 3 (a), Sec. 21, in Munkres' TOPOLOGY, 2nd ed: A Finite Cartesian Product Of Metrizable Spaces Is Metrizable

Prob. 3 (b), Sec. 21, in Munkres' TOPOLOGY, 2nd ed: A Countably Infinite Cartesian Product Of Metrizable Spaces Is Metrizable

A product topology where we allow countably many open sets

If $X=\prod_{i \in I}X_i$ is regular, then $X_i$ is regular for every $i\in I$

Prove that the product topology on $X \times Y$ need not be the co-finite topology.

Show that $X=\prod X_\alpha$ is path connected if and only if each $X_\alpha$ is path connected

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