Question

Prove that every compact subspace of a locally compact space $X$ has a compact neighbourhood

score 111 · Answer 1 · 2021-02-24 17:43:02

111

Views

Prove that every compact subspace of a locally compact space $X$ has a compact neighbourhood

Published on 24 Feb 2021 - 17:43

score 202 · Answer 2 · 2021-03-16 21:15:53

202

Views

Pontryagin Duality and Injective Direct Limits

Published on 16 Mar 2021 - 21:15

score 202 · Answer 3 · 2026-03-27 05:41:54

202

Views

How does Riesz representation theorem give us the left invariance of the Radon measure from a left invariant positive linear functional on $C_c(G)$?

Published on 27 Mar 2026 - 5:41

score 40 · Answer 4 · 2021-04-05 05:17:32

40

Views

$f \in C_c(G) \implies \tilde f \in C_c(G)$ where $ \tilde f(x):=\int_K \int_Kf(k_1xk_2) dk_1dk_2$

Published on 05 Apr 2021 - 5:17

score 46 · Answer 5 · 2021-04-17 13:28:29

46

Views

What is the need of mentioning continuity in the proof of Frobenius reciprocity?

Published on 17 Apr 2021 - 13:28

score 124 · Answer 6 · 2021-04-19 11:40:50

124

Views

Can someone provide intuition for Alfsen's proof of the existence and uniqueness of the Haar measure on locally compact groups?

Published on 19 Apr 2021 - 11:40

score 130 · Answer 7 · 2021-04-30 20:46:31

130

Views

Folland: Find Irreducible Representations of $SU(2)$ and decomposition of $L^2$ via Fourier analysis on compact groups.

Published on 30 Apr 2021 - 20:46

score 111 · Answer 8 · 2021-05-02 16:56:37

111

Views

Why does the dual space consisting of unitary equivalence classes of irreducible representations of compact $G$ not form a group?

Published on 02 May 2021 - 16:56

score 240 · Answer 9 · 2021-05-02 23:10:48

240

Views

Is the set of integers locally compact

Published on 02 May 2021 - 23:10

score 100 · Answer 10 · 2021-05-17 17:09:22

100

Views

A (Radon) Haar measure which is not regular

Published on 17 May 2021 - 17:09

score 160 · Answer 11 · 2021-05-20 10:05:25

160

Views

Discreteness of Pontryagin dual of compact abelian group

Published on 20 May 2021 - 10:05

score 68 · Answer 12 · 2021-05-20 14:49:02

68

Views

If $G$ is a subgroup of the circle, then why is $\{(\text{id}\colon G\to\mathbb{T})^{n}:n\in\mathbb{Z}\}$ dense in the dual $\widehat{G}$?

Published on 20 May 2021 - 14:49

score 77 · Answer 13 · 2021-05-21 21:02:19

77

Views

Can we find a topological group isomorphism $\overline{\{a^{k}:k\in\mathbb{Z}\}}\to\overline{\{b^{k}:k\in\mathbb{Z}\}}$ such that $a\mapsto b$?

Published on 21 May 2021 - 21:02

score 68 · Answer 14 · 2021-06-05 20:01:06

68

Views

Splitting of Compact Group Extensions in Iwasawa's Paper

Published on 05 Jun 2021 - 20:01

score 97 · Answer 15 · 2021-06-29 17:39:11

97

Views

Algebraic tensor product $C_c(G)\otimes X$ dense in $C_c(G,X)$ w.r.t. $\|\cdot\|_1$, where $G$ is a locally compact group and $X$ a Banach space

Published on 29 Jun 2021 - 17:39

List Question

Prove that every compact subspace of a locally compact space $X$ has a compact neighbourhood

Pontryagin Duality and Injective Direct Limits

How does Riesz representation theorem give us the left invariance of the Radon measure from a left invariant positive linear functional on $C_c(G)$?

$f \in C_c(G) \implies \tilde f \in C_c(G)$ where $ \tilde f(x):=\int_K \int_Kf(k_1xk_2) dk_1dk_2$

What is the need of mentioning continuity in the proof of Frobenius reciprocity?

Can someone provide intuition for Alfsen's proof of the existence and uniqueness of the Haar measure on locally compact groups?

Folland: Find Irreducible Representations of $SU(2)$ and decomposition of $L^2$ via Fourier analysis on compact groups.

Why does the dual space consisting of unitary equivalence classes of irreducible representations of compact $G$ not form a group?

Is the set of integers locally compact

A (Radon) Haar measure which is not regular

Discreteness of Pontryagin dual of compact abelian group

If $G$ is a subgroup of the circle, then why is $\{(\text{id}\colon G\to\mathbb{T})^{n}:n\in\mathbb{Z}\}$ dense in the dual $\widehat{G}$?

Can we find a topological group isomorphism $\overline{\{a^{k}:k\in\mathbb{Z}\}}\to\overline{\{b^{k}:k\in\mathbb{Z}\}}$ such that $a\mapsto b$?

Splitting of Compact Group Extensions in Iwasawa's Paper

Algebraic tensor product $C_c(G)\otimes X$ dense in $C_c(G,X)$ w.r.t. $\|\cdot\|_1$, where $G$ is a locally compact group and $X$ a Banach space

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