Question

Measurability of diagonal set originated from Reflection Principle of Brownian motion

score 52 · Answer 1 · 2022-10-22 14:55:05

52

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Measurability of diagonal set originated from Reflection Principle of Brownian motion

Published on 22 Oct 2022 - 14:55

score 69 · Answer 2 · 2026-02-23 04:53:25

69

Views

Difficulty in showing continuity of a function in different topologies

Published on 23 Feb 2026 - 4:53

score 167 · Answer 3 · 2022-10-26 05:40:46

167

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When does $(X\times Y,\Vert\cdot\Vert)$ have the product topology?

Published on 26 Oct 2022 - 5:40

score 62 · Answer 4 · 2026-02-23 10:02:50

62

Views

$\mathbb{R}_{\rm Sorg.}$ is paracompact but $\mathbb{R}_{\rm Sorg.} \times \mathbb{R}_{\rm Sorg.}$ is not

Published on 23 Feb 2026 - 10:02

score 54 · Answer 5 · 2022-10-31 08:50:56

54

Views

Let $X = (-1,1)^{\Bbb N}$ have the product topology. Is the subset $(0,1)^{\Bbb N}$ open?

Published on 31 Oct 2022 - 8:50

score 198 · Answer 6 · 2026-02-23 06:38:39

198

Views

Characterizations of product topology and box topology

Published on 23 Feb 2026 - 6:38

score 84 · Answer 7 · 2022-11-01 15:32:27

84

Views

Connectedness of the set of continuous bijections $\Bbb R^n \to \Bbb R^n$

Published on 01 Nov 2022 - 15:32

score 50 · Answer 8 · 2022-11-08 20:52:49

50

Views

Let $X = \{ f \in \Bbb Q^\Bbb R : \sum_{x \in \Bbb R} |f(x)| < \infty \}$. Show that no sequence in $X$ converges to the constant function $1$.

Published on 08 Nov 2022 - 20:52

score 91 · Answer 9 · 2022-11-08 22:35:22

91

Views

Is the factor of a topological product closed in the product topology?

Published on 08 Nov 2022 - 22:35

score 82 · Answer 10 · 2022-11-09 12:44:51

82

Views

Which of the following subsets of $\mathbb{R}^{\omega}$ are open sets in product topology?

Published on 09 Nov 2022 - 12:44

score 88 · Answer 11 · 2022-11-10 14:21:38

88

Views

$(X\times [0,1])/\sim$ homeomorphic to $X\times S^1$

Published on 10 Nov 2022 - 14:21

score 340 · Answer 12 · 2022-11-10 17:36:28

340

Views

Defining an Embedding in the Product Topology $f: X \to X \times Y$ and $f(x) = x \times y_0$ for $y_0 \in Y$

Published on 10 Nov 2022 - 17:36

score 31 · Answer 13 · 2022-11-11 04:50:19

A property of a subset of the topological space $Y = \Pi_{n \in \mathbb{N}} X_n,$ where each $X_n$ is the Euclidean topology on $\mathbb{R}$

score 30 · Answer 14 · 2022-11-18 09:48:42

How do you determine the function representing the surjective map say for example $f: C\to S$ where $S=\left\{(x,y) \in R^2 : x^2+y^2=r^2\right\}\,?$

score 110 · Answer 15 · 2022-11-20 09:44:51

110

Views

Class of cylinder sets and sigma algebra

Published on 20 Nov 2022 - 9:44

List Question

Measurability of diagonal set originated from Reflection Principle of Brownian motion

Difficulty in showing continuity of a function in different topologies

When does $(X\times Y,\Vert\cdot\Vert)$ have the product topology?

$\mathbb{R}_{\rm Sorg.}$ is paracompact but $\mathbb{R}_{\rm Sorg.} \times \mathbb{R}_{\rm Sorg.}$ is not

Let $X = (-1,1)^{\Bbb N}$ have the product topology. Is the subset $(0,1)^{\Bbb N}$ open?

Characterizations of product topology and box topology

Connectedness of the set of continuous bijections $\Bbb R^n \to \Bbb R^n$

Let $X = \{ f \in \Bbb Q^\Bbb R : \sum_{x \in \Bbb R} |f(x)| < \infty \}$. Show that no sequence in $X$ converges to the constant function $1$.

Is the factor of a topological product closed in the product topology?

Which of the following subsets of $\mathbb{R}^{\omega}$ are open sets in product topology?

$(X\times [0,1])/\sim$ homeomorphic to $X\times S^1$

Defining an Embedding in the Product Topology $f: X \to X \times Y$ and $f(x) = x \times y_0$ for $y_0 \in Y$

A property of a subset of the topological space $Y = \Pi_{n \in \mathbb{N}} X_n,$ where each $X_n$ is the Euclidean topology on $\mathbb{R}$

How do you determine the function representing the surjective map say for example $f: C\to S$ where $S=\left\{(x,y) \in R^2 : x^2+y^2=r^2\right\}\,?$

Class of cylinder sets and sigma algebra

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