Question

Is $A=\{f(x)\in\mathbb{R} : ||x||=1\}$ an interval if $f:\mathbb{R}^2\mapsto \mathbb{R}$ is continous?

score 118 · Answer 1 · 2026-04-15 20:03:19

118

Views

Is $A=\{f(x)\in\mathbb{R} : ||x||=1\}$ an interval if $f:\mathbb{R}^2\mapsto \mathbb{R}$ is continous?

Published on 15 Apr 2026 - 20:03

score 326 · Answer 2 · 2026-05-05 05:04:37

326

Views

A net has a limit if and only if all of its subnets have limits (without the use of Cauchy nets)

Published on 05 May 2026 - 5:04

score 241 · Answer 3 · 2026-03-25 11:00:44

241

Views

Borel measure determined uniquely on a base

Published on 25 Mar 2026 - 11:00

score 172 · Answer 4 · 2026-04-16 05:57:09

172

Views

Let $U$ be the set of all $n×n$ matrices with real entries such that all their eigenvalues belong to $\mathbb C \setminus \mathbb R $.

Published on 16 Apr 2026 - 5:57

score 125 · Answer 5 · 2026-04-12 00:57:00

125

Views

Relative homology and limit

Published on 12 Apr 2026 - 0:57

score 52 · Answer 6 · 2026-04-14 17:48:08

A contradictory result from a corollary with the fact that the quotient space of a Hausdorff space is not necessary Hausdorff

score 40 · Answer 7 · 2026-04-12 10:40:17

40

Views

Are Cat. II sets measurable (for a given outer measure)

Published on 12 Apr 2026 - 10:40

score 183 · Answer 8 · 2026-04-11 08:39:52

183

Views

Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets

Published on 11 Apr 2026 - 8:39

score 1.4k · Answer 9 · 2026-04-16 10:14:36

1.4k

Views

Why is the classification of topological spaces up to homeomorphism impossible or undesirable?

Published on 16 Apr 2026 - 10:14

score 709 · Answer 10 · 2026-04-16 12:42:26

709

Views

Show that given a proper map, for each closed set F its image f(F) is closed

Published on 16 Apr 2026 - 12:42

score 374 · Answer 11 · 2026-04-14 07:21:22

374

Views

Show that the quotient space is homeomorphic to the n-disc

Published on 14 Apr 2026 - 7:21

score 89 · Answer 12 · 2026-04-16 06:29:21

89

Views

Quotient map $f$ from the $n$-sphere to the $n$-disk

Published on 16 Apr 2026 - 6:29

score 133 · Answer 13 · 2026-04-13 21:19:48

133

Views

Every nonempty open subset of $S^{n-1}$ contains an (open) subset whose complement is a $(n-1)$-cell

Published on 13 Apr 2026 - 21:19

score 320 · Answer 14 · 2026-04-14 03:15:10

320

Views

Hawaiian earring as inverse and direct limit

Published on 14 Apr 2026 - 3:15

score 314 · Answer 15 · 2026-04-15 05:35:14

314

Views

Prove the mapping $(x,y)\mapsto x+y$ from $X \times X \to X$ is continuous when $X$ is given a weak topology.

Published on 15 Apr 2026 - 5:35

List Question

Is $A=\{f(x)\in\mathbb{R} : ||x||=1\}$ an interval if $f:\mathbb{R}^2\mapsto \mathbb{R}$ is continous?

A net has a limit if and only if all of its subnets have limits (without the use of Cauchy nets)

Borel measure determined uniquely on a base

Let $U$ be the set of all $n×n$ matrices with real entries such that all their eigenvalues belong to $\mathbb C \setminus \mathbb R $.

Relative homology and limit

A contradictory result from a corollary with the fact that the quotient space of a Hausdorff space is not necessary Hausdorff

Are Cat. II sets measurable (for a given outer measure)

Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets

Why is the classification of topological spaces up to homeomorphism impossible or undesirable?

Show that given a proper map, for each closed set F its image f(F) is closed

Show that the quotient space is homeomorphic to the n-disc

Quotient map $f$ from the $n$-sphere to the $n$-disk

Every nonempty open subset of $S^{n-1}$ contains an (open) subset whose complement is a $(n-1)$-cell

Hawaiian earring as inverse and direct limit

Prove the mapping $(x,y)\mapsto x+y$ from $X \times X \to X$ is continuous when $X$ is given a weak topology.

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