Question

If $d(x_n,A)\to0$ can we conclude $(x_n)$ has a cluster point in $A?$

score 50 · Answer 1 · 2026-04-15 17:56:17

50

Views

If $d(x_n,A)\to0$ can we conclude $(x_n)$ has a cluster point in $A?$

Published on 15 Apr 2026 - 17:56

score 74 · Answer 2 · 2026-04-15 12:52:10

74

Views

$\mathbb{C}$ similar to $\mathbb{R^2}$ for some properties

Published on 15 Apr 2026 - 12:52

score 154 · Answer 3 · 2026-04-09 01:02:13

154

Views

compact and closed set problem

Published on 09 Apr 2026 - 1:02

score 317 · Answer 4 · 2026-04-09 14:25:47

317

Views

Example for why K being compact needed.

Published on 09 Apr 2026 - 14:25

score 181 · Answer 5 · 2026-04-11 08:00:01

181

Views

Cover a compact set with closed balls

Published on 11 Apr 2026 - 8:00

score 50 · Answer 6 · 2026-04-16 09:55:14

If Λ is a open subset of a metric space and $K⊆Λ_ε:=\{x:d(x,Λ^c)>ε\}$ is compact, is there a compact $L⊆Λ_ε$ s.t. $B_δ(x)⊆L$ for all $x∈K$?

score 387 · Answer 7 · 2026-04-14 21:43:46

387

Views

Closed unit ball in $ L^2 ([0, 1]) $ intersect the set of $1$-Lipschitz functions is compact in the $ L^2 $ norm.

Published on 14 Apr 2026 - 21:43

score 439 · Answer 8 · 2026-04-17 13:26:27

439

Views

Is unsorted first-order logic equivalently expressive to infinitely-many-sorted first-order logic?

Published on 17 Apr 2026 - 13:26

score 140 · Answer 9 · 2026-05-10 14:29:12

140

Views

Countably Compact, Separable, $T_1$, Connected Space that is not Compact

Published on 10 May 2026 - 14:29

score 317 · Answer 10 · 2026-05-11 07:46:53

317

Views

If $X$ admits a Hausdorff compactification, then $X$ is locally compact?

Published on 11 May 2026 - 7:46

score 251 · Answer 11 · 2026-05-14 23:26:45

251

Views

Convergence and compactness of $f_n(t) = \sin (\sqrt{t + 4n^2\pi})$.

Published on 14 May 2026 - 23:26

score 416 · Answer 12 · 2026-05-10 16:35:48

416

Views

Given an open subset of a Riemannian manifold, is the group of isometries that extend to a global isometry closed?

Published on 10 May 2026 - 16:35

score 825 · Answer 13 · 2026-04-12 19:24:30

825

Views

Prove that a graph of a continuous function on a compact set is compact

Published on 12 Apr 2026 - 19:24

score 134 · Answer 14 · 2026-04-11 05:45:49

134

Views

Compactness Definition Concerning Accumulation Points

Published on 11 Apr 2026 - 5:45

score 374 · Answer 15 · 2026-05-10 14:56:57

374

Views

Convergence of iterated functions like Collatz in a Compact metric space

Published on 10 May 2026 - 14:56

List Question

If $d(x_n,A)\to0$ can we conclude $(x_n)$ has a cluster point in $A?$

$\mathbb{C}$ similar to $\mathbb{R^2}$ for some properties

compact and closed set problem

Example for why K being compact needed.

Cover a compact set with closed balls

If Λ is a open subset of a metric space and $K⊆Λ_ε:=\{x:d(x,Λ^c)>ε\}$ is compact, is there a compact $L⊆Λ_ε$ s.t. $B_δ(x)⊆L$ for all $x∈K$?

Closed unit ball in $ L^2 ([0, 1]) $ intersect the set of $1$-Lipschitz functions is compact in the $ L^2 $ norm.

Is unsorted first-order logic equivalently expressive to infinitely-many-sorted first-order logic?

Countably Compact, Separable, $T_1$, Connected Space that is not Compact

If $X$ admits a Hausdorff compactification, then $X$ is locally compact?

Convergence and compactness of $f_n(t) = \sin (\sqrt{t + 4n^2\pi})$.

Given an open subset of a Riemannian manifold, is the group of isometries that extend to a global isometry closed?

Prove that a graph of a continuous function on a compact set is compact

Compactness Definition Concerning Accumulation Points

Convergence of iterated functions like Collatz in a Compact metric space

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