List questions from product-space

Published on 17 Mar 2026 - 3:53

183

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Set of Positive Sequences that Sum to 1 is Compact under Product Topology?

Published on 20 Mar 2026 - 2:24

1.1k

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$ \prod_{j \in J} X_{j} $ is locally connected if, and only if, each $ X_{j} $ is locally connected ...

Published on 20 Mar 2026 - 12:05

906

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Dense subspaces of $L^\infty(\Omega\times\Omega)$

Published on 23 Mar 2026 - 7:12

100

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$\{0,1\}^{\mathbb{N}}$ homeomorphic to $\mathbb{R}$?

Published on 25 Mar 2026 - 0:41

82

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Understanding product topology

Published on 23 Mar 2026 - 12:47

749

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The topology generated by the metric is the product topology of discrete space {0,1}

Published on 23 Mar 2026 - 0:31

103

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Show that $(X,d)$ is compact

Published on 24 Mar 2026 - 4:02

175

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For a discrete topological space $X$, is Perm$(X)$ a topological group as a subspace of product topological space $X^X$?

Published on 22 Mar 2026 - 18:27

190

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Uniform distribution Measure

Published on 25 Mar 2026 - 1:42

104

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Show that the addition function for two elements in $\mathbb{R}^\omega$ is continuous

Published on 24 Mar 2026 - 22:44

114

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$\operatorname{cl}(A \times B) = \operatorname{cl}_X(A) \times \operatorname{cl}_Y(B)$

Published on 25 Mar 2026 - 1:18

265

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Proving the Fubini-Tonelli Theorem

Published on 25 Mar 2026 - 3:00

239

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Connectedness in Product Topology via Simple Chain

Published on 25 Mar 2026 - 3:57

67

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Understanding the continuity of the projection $\pi:\mathbb{R^2} \to \mathbb{R}$

Published on 25 Mar 2026 - 3:07

List Question

Open Set in Product Space Takes a Certain Form

Set of Positive Sequences that Sum to 1 is Compact under Product Topology?

$ \prod_{j \in J} X_{j} $ is locally connected if, and only if, each $ X_{j} $ is locally connected ...

Dense subspaces of $L^\infty(\Omega\times\Omega)$

$\{0,1\}^{\mathbb{N}}$ homeomorphic to $\mathbb{R}$?

Understanding product topology

The topology generated by the metric is the product topology of discrete space {0,1}

Show that $(X,d)$ is compact

For a discrete topological space $X$, is Perm$(X)$ a topological group as a subspace of product topological space $X^X$?

Uniform distribution Measure

Show that the addition function for two elements in $\mathbb{R}^\omega$ is continuous

$\operatorname{cl}(A \times B) = \operatorname{cl}_X(A) \times \operatorname{cl}_Y(B)$

Proving the Fubini-Tonelli Theorem

Connectedness in Product Topology via Simple Chain

Understanding the continuity of the projection $\pi:\mathbb{R^2} \to \mathbb{R}$

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