List questions from product-space

Published on 23 Feb 2026 - 8:38

81

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Continuity of a bilinear form with respect to weak$^*$ topology

Published on 31 Dec 2021 - 6:13

39

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Confusion over the metric in the product of two topological groups

Published on 04 Jan 2022 - 20:56

82

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Path connected product topology implies every topology is path connected

Published on 06 Jan 2022 - 8:49

68

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How do I prove that a filter converges in a cartesian product?

Published on 07 Jan 2022 - 13:08

38

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Product of paracompact and compact spaces

Published on 23 Feb 2026 - 8:24

67

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Let $g,h : \Bbb R \to \Bbb R$ be any functions. Define $F: \Bbb R^{\Bbb R} \to \Bbb R^{\Bbb R}$ as $F(f)(t)=g(t)f(h(t))$. Show that $F$ is continuous.

Published on 10 Jan 2022 - 20:59

161

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Let $X= \Bbb R^{\Bbb N}$ and let $A\subset X$ be the set of bounded sequences. Is $A$ open/closed in the product topology of $\Bbb R^{\Bbb N}$?

Published on 12 Jan 2022 - 11:36

80

Views

Prove, that the topology of $X$ coinduced by maps $f_i$ from the usual topology of $\Bbb R$ is finer than the one $X$ inherited from $\Bbb R^{\Bbb N}$

Published on 13 Jan 2022 - 18:17

38

Views

Is restriction of a projection to a connected subset a quotient map?

Published on 20 Jan 2022 - 3:26

88

Views

Density of sets in the product space $X= \Bbb R^{\Bbb R}$

Published on 23 Jan 2022 - 15:46

81

Views

How do I prove this statement about the continuity of the product map?

Published on 27 Jan 2022 - 21:50

41

Views

How do I show this statement about convergence in filters?

Published on 29 Jan 2022 - 19:26

178

Views

Find closure of sets w.r.t product topology?

Published on 04 Feb 2022 - 8:39

331

Views

A proof of Tychonoff theorem from Alexander subbase theorem

Published on 05 Feb 2022 - 14:33

List Question

One question in Spanier's Algebraic Topology Theorem 1.4.12

Continuity of a bilinear form with respect to weak$^*$ topology

Confusion over the metric in the product of two topological groups

Path connected product topology implies every topology is path connected

How do I prove that a filter converges in a cartesian product?

Product of paracompact and compact spaces

Let $g,h : \Bbb R \to \Bbb R$ be any functions. Define $F: \Bbb R^{\Bbb R} \to \Bbb R^{\Bbb R}$ as $F(f)(t)=g(t)f(h(t))$. Show that $F$ is continuous.

Let $X= \Bbb R^{\Bbb N}$ and let $A\subset X$ be the set of bounded sequences. Is $A$ open/closed in the product topology of $\Bbb R^{\Bbb N}$?

Prove, that the topology of $X$ coinduced by maps $f_i$ from the usual topology of $\Bbb R$ is finer than the one $X$ inherited from $\Bbb R^{\Bbb N}$

Is restriction of a projection to a connected subset a quotient map?

Density of sets in the product space $X= \Bbb R^{\Bbb R}$

How do I prove this statement about the continuity of the product map?

How do I show this statement about convergence in filters?

Find closure of sets w.r.t product topology?

A proof of Tychonoff theorem from Alexander subbase theorem

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