Question

Show that $F = \{\lambda x|\lambda\in \mathbb{R}_+, x\in K\}$ is closed where $K$ is a compact set.

score 92 · Answer 1 · 2026-04-15 04:12:10

92

Views

Show that $F = \{\lambda x|\lambda\in \mathbb{R}_+, x\in K\}$ is closed where $K$ is a compact set.

Published on 15 Apr 2026 - 4:12

score 140 · Answer 2 · 2026-04-10 22:40:12

140

Views

Does boundedness imply total boundedness?

Published on 10 Apr 2026 - 22:40

score 27 · Answer 3 · 2026-04-12 14:17:17

27

Views

Example of two non-homeomorphic spaces with two continual mappings between them

Published on 12 Apr 2026 - 14:17

score 95 · Answer 4 · 2026-04-10 18:11:21

95

Views

Equicontinuous family of functions

Published on 10 Apr 2026 - 18:11

score 152 · Answer 5 · 2026-04-12 14:14:29

152

Views

Proof that Separable Banach Spaces are Homeomorphic and Continuum Hypothesis

Published on 12 Apr 2026 - 14:14

score 43 · Answer 6 · 2026-04-12 12:04:35

43

Views

Separation from family of closed and connected subsets

Published on 12 Apr 2026 - 12:04

score 369 · Answer 7 · 2026-04-14 18:48:21

369

Views

Show that the unbounded region determined by a closed curve is doubly connected

Published on 14 Apr 2026 - 18:48

score 1.3k · Answer 8 · 2026-04-23 05:33:39

1.3k

Views

Lindelöf and separable metric space

Published on 23 Apr 2026 - 5:33

score 645 · Answer 9 · 2026-04-29 12:56:00

645

Views

Number of real roots of a quintic equation

Published on 29 Apr 2026 - 12:56

score 139 · Answer 10 · 2026-03-25 07:48:52

139

Views

Is the algebra map of the ultrafilter monad continuous?

Published on 25 Mar 2026 - 7:48

score 1.5k · Answer 11 · 2026-04-25 17:33:59

1.5k

Views

Prove that $\mathbb{R}^2\setminus E$ is path-connected

Published on 25 Apr 2026 - 17:33

score 1.3k · Answer 12 · 2026-04-16 06:54:40

1.3k

Views

If $A$ and $B$ are isomorphic and $C$ and $D$ are isomorphic, then $A\times C$ and $B\times D$ are isomorphic?

Published on 16 Apr 2026 - 6:54

score 453 · Answer 13 · 2026-04-15 10:01:40

453

Views

Show that all open sets in $\mathbb{R}^n$ are the same for metrics $d_1,d_2,d_\infty$

Published on 15 Apr 2026 - 10:01

score 4.7k · Answer 14 · 2026-04-16 15:09:10

4.7k

Views

Is $\Bbb Q$ intersect $[0,1]$ in $\Bbb R$ compact?

Published on 16 Apr 2026 - 15:09

score 107 · Answer 15 · 2026-04-12 00:13:07

107

Views

Homeomorphism between two topologies, one finer than the other

Published on 12 Apr 2026 - 0:13

List Question

Show that $F = \{\lambda x|\lambda\in \mathbb{R}_+, x\in K\}$ is closed where $K$ is a compact set.

Does boundedness imply total boundedness?

Example of two non-homeomorphic spaces with two continual mappings between them

Equicontinuous family of functions

Proof that Separable Banach Spaces are Homeomorphic and Continuum Hypothesis

Separation from family of closed and connected subsets

Show that the unbounded region determined by a closed curve is doubly connected

Lindelöf and separable metric space

Number of real roots of a quintic equation

Is the algebra map of the ultrafilter monad continuous?

Prove that $\mathbb{R}^2\setminus E$ is path-connected

If $A$ and $B$ are isomorphic and $C$ and $D$ are isomorphic, then $A\times C$ and $B\times D$ are isomorphic?

Show that all open sets in $\mathbb{R}^n$ are the same for metrics $d_1,d_2,d_\infty$

Is $\Bbb Q$ intersect $[0,1]$ in $\Bbb R$ compact?

Homeomorphism between two topologies, one finer than the other

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