Question

Topology: continuity on product of (metric) spaces

score 144 · Answer 1 · 2026-03-25 06:04:33

144

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Topology: continuity on product of (metric) spaces

Published on 25 Mar 2026 - 6:04

score 823 · Answer 2 · 2026-03-28 20:05:36

823

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

Published on 28 Mar 2026 - 20:05

score 354 · Answer 3 · 2018-07-02 01:13:10

354

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Show $F:C[0,1] \rightarrow C[0,1]$ defined by $F(f) = g \circ f$ is continuous.

Published on 02 Jul 2018 - 1:13

score 58 · Answer 4 · 2018-07-02 12:22:12

58

Views

Extending continuity on $\mathbb{R}$ to continuity on $\overline{\mathbb{R}}= \mathbb{R} \cup \{-\infty,+\infty\}$

Published on 02 Jul 2018 - 12:22

score 621 · Answer 5 · 2018-07-02 16:38:38

621

Views

Showing that a function has the intermediate value property

Published on 02 Jul 2018 - 16:38

score 83 · Answer 6 · 2026-03-25 09:29:04

83

Views

Show that $\operatorname{Im} f$ is a union of two disjoint intervals

Published on 25 Mar 2026 - 9:29

score 62 · Answer 7 · 2018-07-03 13:31:00

62

Views

Let $F(x) = \int_{-\infty}^xf(t)dt,\;$. If $f(x)$ is discontinuous at $x=c$, then is $F(x)$ not differentiable at $x=c$

Published on 03 Jul 2018 - 13:31

score 677 · Answer 8 · 2018-07-03 18:23:17

677

Views

Maximum/Minimum theorem

Published on 03 Jul 2018 - 18:23

score 903 · Answer 9 · 2026-03-28 20:07:48

903

Views

Metrizability of Hausdorff continuous image of compact metric space

Published on 28 Mar 2026 - 20:07

score 39 · Answer 10 · 2026-03-29 20:12:19

39

Views

Show that a function on invertible operators is continuous

Published on 29 Mar 2026 - 20:12

score 51 · Answer 11 · 2018-07-04 09:34:42

51

Views

Using polar coordinates to show continuity of a multivariable function with pole not at zero

Published on 04 Jul 2018 - 9:34

score 211 · Answer 12 · 2026-03-31 05:49:30

211

Views

Question about proof of intermediate value theorem

Published on 31 Mar 2026 - 5:49

score 37 · Answer 13 · 2026-03-27 08:27:03

37

Views

How to make my analysis more rigorous?

Published on 27 Mar 2026 - 8:27

score 173 · Answer 14 · 2026-03-25 12:21:12

173

Views

Proof Irrational number $x$, given $N\in{\mathbb{N}}$ exists $\epsilon>0$ so all rationals $\in{V_\epsilon{(x)}}$ have denominator larger than N.

Published on 25 Mar 2026 - 12:21

score 296 · Answer 15 · 2018-07-05 14:47:33

296

Views

Cantor Set Function $g(x)=1$ ($x\in{C}$), $g(x)=0$ ($x$ not in C) (Dis)Continuity

Published on 05 Jul 2018 - 14:47

List Question

Topology: continuity on product of (metric) spaces

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

Show $F:C[0,1] \rightarrow C[0,1]$ defined by $F(f) = g \circ f$ is continuous.

Extending continuity on $\mathbb{R}$ to continuity on $\overline{\mathbb{R}}= \mathbb{R} \cup \{-\infty,+\infty\}$

Showing that a function has the intermediate value property

Show that $\operatorname{Im} f$ is a union of two disjoint intervals

Let $F(x) = \int_{-\infty}^xf(t)dt,\;$. If $f(x)$ is discontinuous at $x=c$, then is $F(x)$ not differentiable at $x=c$

Maximum/Minimum theorem

Metrizability of Hausdorff continuous image of compact metric space

Show that a function on invertible operators is continuous

Using polar coordinates to show continuity of a multivariable function with pole not at zero

Question about proof of intermediate value theorem

How to make my analysis more rigorous?

Proof Irrational number $x$, given $N\in{\mathbb{N}}$ exists $\epsilon>0$ so all rationals $\in{V_\epsilon{(x)}}$ have denominator larger than N.

Cantor Set Function $g(x)=1$ ($x\in{C}$), $g(x)=0$ ($x$ not in C) (Dis)Continuity

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