Question

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

score 47 · Answer 1 · 2018-06-17 04:05:10

47

Views

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

Published on 17 Jun 2018 - 4:05

score 71 · Answer 2 · 2018-06-17 14:47:14

71

Views

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

Published on 17 Jun 2018 - 14:47

score 151 · Answer 3 · 2018-06-17 23:52:02

151

Views

compact and closed set problem

Published on 17 Jun 2018 - 23:52

score 314 · Answer 4 · 2018-06-19 19:16:54

314

Views

Example for why K being compact needed.

Published on 19 Jun 2018 - 19:16

score 178 · Answer 5 · 2018-06-21 20:00:42

178

Views

Cover a compact set with closed balls

Published on 21 Jun 2018 - 20:00

score 47 · Answer 6 · 2018-06-22 10:14:05

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 384 · Answer 7 · 2018-06-23 21:07:44

384

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 23 Jun 2018 - 21:07

score 435 · Answer 8 · 2026-03-25 15:46:11

435

Views

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

Published on 25 Mar 2026 - 15:46

score 137 · Answer 9 · 2026-03-25 09:48:19

137

Views

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

Published on 25 Mar 2026 - 9:48

score 315 · Answer 10 · 2026-03-25 20:42:23

315

Views

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

Published on 25 Mar 2026 - 20:42

score 248 · Answer 11 · 2026-03-28 12:14:24

248

Views

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

Published on 28 Mar 2026 - 12:14

score 413 · Answer 12 · 2026-03-25 04:43:37

413

Views

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

Published on 25 Mar 2026 - 4:43

score 822 · Answer 13 · 2018-07-01 17:43:12

822

Views

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

Published on 01 Jul 2018 - 17:43

score 131 · Answer 14 · 2018-07-01 21:03:50

131

Views

Compactness Definition Concerning Accumulation Points

Published on 01 Jul 2018 - 21:03

score 371 · Answer 15 · 2026-03-25 06:05:32

371

Views

Convergence of iterated functions like Collatz in a Compact metric space

Published on 25 Mar 2026 - 6:05

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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