Question

Definition of Product Topology

score 6.6k · Answer 1 · 2017-01-06 14:24:33

6.6k

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Definition of Product Topology

Published on 06 Jan 2017 - 14:24

score 224 · Answer 2 · 2017-01-13 13:32:01

224

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Is it true that $X \times I \sim Y \times I \Longrightarrow X \sim Y$?

Published on 13 Jan 2017 - 13:32

score 89 · Answer 3 · 2017-01-16 18:40:22

89

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Closure in A Product topological space $\overline{A_1\times A_2}=\overline{A_1}\times\overline{A_2}$

Published on 16 Jan 2017 - 18:40

score 287 · Answer 4 · 2017-01-18 12:34:31

287

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Equivalence of the Box and product topologies on a finite product

Published on 18 Jan 2017 - 12:34

score 391 · Answer 5 · 2017-01-31 18:22:14

391

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Understanding the difference between basis, topology, and open sets in finite products

Published on 31 Jan 2017 - 18:22

score 239 · Answer 6 · 2017-02-15 17:44:26

239

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Finite intersection of inverse projections of open sets equal to Cartesian product.

Published on 15 Feb 2017 - 17:44

score 1.6k · Answer 7 · 2026-02-23 03:18:56

1.6k

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(Proof) Product of Lindelöf and compact set is Lindelöf

Published on 23 Feb 2026 - 3:18

score 53 · Answer 8 · 2017-03-06 14:00:42

53

Views

Hausdorffness of product space

Published on 06 Mar 2017 - 14:00

score 573 · Answer 9 · 2017-03-20 03:18:26

573

Views

Convergent sequences in Cartesian product

Published on 20 Mar 2017 - 3:18

score 154 · Answer 10 · 2017-03-20 19:35:46

154

Views

Formula for slices of interior in a product space

Published on 20 Mar 2017 - 19:35

score 2.6k · Answer 11 · 2026-02-24 13:37:24

2.6k

Views

Pointwise convergence equivalent to convergence in pointwise topology

Published on 24 Feb 2026 - 13:37

score 94 · Answer 12 · 2023-02-10 15:11:54

94

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Product topology and relativization

Published on 10 Feb 2023 - 15:11

score 181 · Answer 13 · 2026-03-26 01:29:18

181

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Let $X$ be a topological space such that $X \times \mathbb{R}$ is homeomorphic to $\mathbb{R}^2$. Must $X$ be homeomorphic to $\mathbb{R}$?

Published on 26 Mar 2026 - 1:29

score 355 · Answer 14 · 2023-02-16 08:06:26

355

Views

Linear projections and topological direct sum in normed/Banach spaces

Published on 16 Feb 2023 - 8:06

score 149 · Answer 15 · 2023-02-19 06:14:57

149

Views

Product topology and subspace topology

Published on 19 Feb 2023 - 6:14

List Question

Definition of Product Topology

Is it true that $X \times I \sim Y \times I \Longrightarrow X \sim Y$?

Closure in A Product topological space $\overline{A_1\times A_2}=\overline{A_1}\times\overline{A_2}$

Equivalence of the Box and product topologies on a finite product

Understanding the difference between basis, topology, and open sets in finite products

Finite intersection of inverse projections of open sets equal to Cartesian product.

(Proof) Product of Lindelöf and compact set is Lindelöf

Hausdorffness of product space

Convergent sequences in Cartesian product

Formula for slices of interior in a product space

Pointwise convergence equivalent to convergence in pointwise topology

Product topology and relativization

Let $X$ be a topological space such that $X \times \mathbb{R}$ is homeomorphic to $\mathbb{R}^2$. Must $X$ be homeomorphic to $\mathbb{R}$?

Linear projections and topological direct sum in normed/Banach spaces

Product topology and subspace topology

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