Question

Given $A$ a convex set of $\mathbb{R}^n$ such that $int(A) \neq \emptyset$, prove that $int(cl(A)) = int(A)$.

score 226 · Answer 1 · 2026-03-25 14:36:43

226

Views

Given $A$ a convex set of $\mathbb{R}^n$ such that $int(A) \neq \emptyset$, prove that $int(cl(A)) = int(A)$.

Published on 25 Mar 2026 - 14:36

score 84 · Answer 2 · 2020-03-10 11:32:42

84

Views

Fréchet subspace of LF space

Published on 10 Mar 2020 - 11:32

score 139 · Answer 3 · 2020-03-10 12:38:05

139

Views

Sequential convergence of the compact-open topology, where the codomain has weak topology.

Published on 10 Mar 2020 - 12:38

score 149 · Answer 4 · 2020-03-10 16:25:10

149

Views

Why is any distribution is the derivative of another distribution?

Published on 10 Mar 2020 - 16:25

score 56 · Answer 5 · 2020-03-12 10:06:22

56

Views

Show that $X'\neq X^*$ for $X$ t.v.s. with $dim X=\infty$ where the neighbourhood filter of $0$ has a countable basis

Published on 12 Mar 2020 - 10:06

score 829 · Answer 6 · 2020-03-12 10:38:25

829

Views

Orthogonal complement of the orthogonal complement

Published on 12 Mar 2020 - 10:38

score 699 · Answer 7 · 2026-03-25 19:11:13

699

Views

Topology of Space of continuous functions with compact support

Published on 25 Mar 2026 - 19:11

score 409 · Answer 8 · 2020-03-13 08:39:37

409

Views

$(X,d)$ is a metric space, prove $C(X)$ is a finite-dimensional vector space $\Leftrightarrow$ $X$ is a finite set

Published on 13 Mar 2020 - 8:39

score 453 · Answer 9 · 2020-03-14 10:27:36

453

Views

What is inheriting of topology? What is the use of studying it?

Published on 14 Mar 2020 - 10:27

score 130 · Answer 10 · 2020-03-15 10:07:04

130

Views

Does there always exist an injective map in the algebraic dual space $X^*$ of an infinite-dimensional t.v.s $X$?

Published on 15 Mar 2020 - 10:07

score 24 · Answer 11 · 2020-03-15 23:20:04

24

Views

Show that : $ h(A, B) = \sup_{x^\in D} |s(x^|A)-s(x^*|B)| $

Published on 15 Mar 2020 - 23:20

score 23 · Answer 12 · 2026-03-25 22:04:49

23

Views

Closure of the Set of Hilbert-Schmidt Operators

Published on 25 Mar 2026 - 22:04

score 23 · Answer 13 · 2020-03-19 17:15:03

23

Views

Is $\{ V_{H,\varepsilon} \mid \varepsilon> 0, H\in \wp_{<\omega}(X)\}$ a filter over $\mathbb C^X$?

Published on 19 Mar 2020 - 17:15

score 142 · Answer 14 · 2020-03-20 01:45:19

142

Views

Proof of the Chain Rule in not normed TVS

Published on 20 Mar 2020 - 1:45

score 57 · Answer 15 · 2020-03-21 03:44:57

57

Views

Is the product of a linear map and a tangent to 0 function a tangent to 0 function?

Published on 21 Mar 2020 - 3:44

List Question

Given $A$ a convex set of $\mathbb{R}^n$ such that $int(A) \neq \emptyset$, prove that $int(cl(A)) = int(A)$.

Fréchet subspace of LF space

Sequential convergence of the compact-open topology, where the codomain has weak topology.

Why is any distribution is the derivative of another distribution?

Show that $X'\neq X^*$ for $X$ t.v.s. with $dim X=\infty$ where the neighbourhood filter of $0$ has a countable basis

Orthogonal complement of the orthogonal complement

Topology of Space of continuous functions with compact support

$(X,d)$ is a metric space, prove $C(X)$ is a finite-dimensional vector space $\Leftrightarrow$ $X$ is a finite set

What is inheriting of topology? What is the use of studying it?

Does there always exist an injective map in the algebraic dual space $X^*$ of an infinite-dimensional t.v.s $X$?

Show that : $ h(A, B) = \sup_{x^\in D} |s(x^|A)-s(x^*|B)| $

Closure of the Set of Hilbert-Schmidt Operators

Is $\{ V_{H,\varepsilon} \mid \varepsilon> 0, H\in \wp_{<\omega}(X)\}$ a filter over $\mathbb C^X$?

Proof of the Chain Rule in not normed TVS

Is the product of a linear map and a tangent to 0 function a tangent to 0 function?

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