Question

Prove that $\overline{f(A)}\subseteq f(\overline{A})$ where $f: X \rightarrow Y$ is continuous, $X$ is compact and $A \subseteq X$

score 395 · Answer 1 · 2016-06-22 17:53:48

395

Views

Prove that $\overline{f(A)}\subseteq f(\overline{A})$ where $f: X \rightarrow Y$ is continuous, $X$ is compact and $A \subseteq X$

Published on 22 Jun 2016 - 17:53

score 121 · Answer 2 · 2026-04-11 15:00:45

121

Views

Is boundedness required in equivalence between $\frac1n\sum_{k=1}^na_k\to0$ and $\frac1n\sum_{k=1}^na_k^2\to0$?

Published on 11 Apr 2026 - 15:00

score 120 · Answer 3 · 2026-03-28 15:11:54

120

Views

Is there a searchable database of mathematical objects that you can search by property?

Published on 28 Mar 2026 - 15:11

score 287 · Answer 4 · 2016-06-25 10:26:00

287

Views

If $f(x,y)$ is a function that its contour lines are straight, is it necessary looks like $f(x,y) = ax + by + c$

Published on 25 Jun 2016 - 10:26

score 112 · Answer 5 · 2016-06-25 20:08:40

112

Views

Is there a measure space $(X,\mathcal M, m)$ such that $\{m(E) \mid E \in \mathcal M\} = \Bbb Q_{\geq 0} \cup \{+\infty\}$?

Published on 25 Jun 2016 - 20:08

score 1.3k · Answer 6 · 2026-04-12 16:47:46

1.3k

Views

Are there any examples of Graphs in nature?

Published on 12 Apr 2026 - 16:47

score 130 · Answer 7 · 2026-04-12 22:44:35

130

Views

Reference request: how to check whether a set is invariant for a second order dynamical system?

Published on 12 Apr 2026 - 22:44

score 71 · Answer 8 · 2026-04-12 18:51:29

71

Views

Find a counter example

Published on 12 Apr 2026 - 18:51

score 1.2k · Answer 9 · 2026-04-09 10:58:37

1.2k

Views

Regular topological spaces need not to be normal

Published on 09 Apr 2026 - 10:58

score 1k · Answer 10 · 2026-04-13 06:54:22

1k

Views

Simple example of a function which is in $W^{1,p}(\Omega)$ but not in $L^{\infty}(\Omega)$?

Published on 13 Apr 2026 - 6:54

score 420 · Answer 11 · 2026-03-27 01:46:38

420

Views

Example of Non-Measurable Sets in Product Space

Published on 27 Mar 2026 - 1:46

score 653 · Answer 12 · 2026-03-30 14:20:04

653

Views

Noteworthy examples of finite categories

Published on 30 Mar 2026 - 14:20

score 310 · Answer 13 · 2026-04-12 17:12:37

310

Views

Counterexamples in Analysis

Published on 12 Apr 2026 - 17:12

score 104 · Answer 14 · 2026-04-13 00:15:00

104

Views

An example of subset $A$ such that $A \cap K$ is open in $K$ for each compact set $K$, but $A$ is not open.

Published on 13 Apr 2026 - 0:15

score 130 · Answer 15 · 2026-04-12 21:59:55

130

Views

Obvious application of internal category theory outside from topoi

Published on 12 Apr 2026 - 21:59

List Question

Prove that $\overline{f(A)}\subseteq f(\overline{A})$ where $f: X \rightarrow Y$ is continuous, $X$ is compact and $A \subseteq X$

Is boundedness required in equivalence between $\frac1n\sum_{k=1}^na_k\to0$ and $\frac1n\sum_{k=1}^na_k^2\to0$?

Is there a searchable database of mathematical objects that you can search by property?

If $f(x,y)$ is a function that its contour lines are straight, is it necessary looks like $f(x,y) = ax + by + c$

Is there a measure space $(X,\mathcal M, m)$ such that $\{m(E) \mid E \in \mathcal M\} = \Bbb Q_{\geq 0} \cup \{+\infty\}$?

Are there any examples of Graphs in nature?

Reference request: how to check whether a set is invariant for a second order dynamical system?

Find a counter example

Regular topological spaces need not to be normal

Simple example of a function which is in $W^{1,p}(\Omega)$ but not in $L^{\infty}(\Omega)$?

Example of Non-Measurable Sets in Product Space

Noteworthy examples of finite categories

Counterexamples in Analysis

An example of subset $A$ such that $A \cap K$ is open in $K$ for each compact set $K$, but $A$ is not open.

Obvious application of internal category theory outside from topoi

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