Question

Is the inverse of bijective continuous functions always continuous?

score 717 · Answer 1 · 2026-03-25 01:26:15

717

Views

Is the inverse of bijective continuous functions always continuous?

Published on 25 Mar 2026 - 1:26

score 243 · Answer 2 · 2026-03-25 11:25:58

243

Views

Why not define lines in a metric space using a locus?

Published on 25 Mar 2026 - 11:25

score 62 · Answer 3 · 2026-03-25 07:15:35

62

Views

Motivation behind proof of Metrizability & local countable basis equivalence

Published on 25 Mar 2026 - 7:15

score 74 · Answer 4 · 2026-03-24 10:58:46

74

Views

Is $\left\lVert f_U-f_V\right\rVert_{op}\leq \left\lVert U-V\right\rVert_2$ where $f_U = A\mapsto UAU^*$?

Published on 24 Mar 2026 - 10:58

score 182 · Answer 5 · 2026-03-24 20:32:08

182

Views

Proof of Existence of Complete Field with Dense Subfield

Published on 24 Mar 2026 - 20:32

score 305 · Answer 6 · 2026-03-27 10:07:30

305

Views

Definition of Compactness

Published on 27 Mar 2026 - 10:07

score 55 · Answer 7 · 2026-03-27 15:10:35

55

Views

Is $\{f \in \mathcal{C}[0,1]| \int_0^\frac{1}{2}f - \int_\frac{1}{2}^1 f = 1\}$ a connected set?

Published on 27 Mar 2026 - 15:10

score 294 · Answer 8 · 2026-03-27 15:11:42

294

Views

Assumption from Tietze's extension theorem as a sufficient condition for a set in metric space to be closed

Published on 27 Mar 2026 - 15:11

score 404 · Answer 9 · 2026-03-27 15:09:14

404

Views

Cantor's intersection theorem with diameters bounded below

Published on 27 Mar 2026 - 15:09

score 88 · Answer 10 · 2026-03-27 18:26:47

88

Views

Why is the set ${\{1\}}$ closed on $\mathbb{R}$ with the metric $d(x,y) = |x−y|$

Published on 27 Mar 2026 - 18:26

score 32 · Answer 11 · 2018-01-29 14:18:38

32

Views

Closure of set in set notation involving a combination of metrics

Published on 29 Jan 2018 - 14:18

score 89 · Answer 12 · 2018-01-29 14:41:26

89

Views

If the space $B(X,Y)$ of bounded function from $X$ into $Y$ is a complete metric space, show that $Y$ is a complete metric space.

Published on 29 Jan 2018 - 14:41

score 980 · Answer 13 · 2026-03-27 03:48:27

980

Views

Finite set implies sequentially compact

Published on 27 Mar 2026 - 3:48

score 1.1k · Answer 14 · 2026-03-27 16:47:49

1.1k

Views

Are all the $\ell^p$ metrics topologically equivalent for positive integer values of $p$?

Published on 27 Mar 2026 - 16:47

score 382 · Answer 15 · 2026-03-22 23:28:10

382

Views

Uniform limit not being equal to pointwise limit?

Published on 22 Mar 2026 - 23:28

List Question

Is the inverse of bijective continuous functions always continuous?

Why not define lines in a metric space using a locus?

Motivation behind proof of Metrizability & local countable basis equivalence

Is $\left\lVert f_U-f_V\right\rVert_{op}\leq \left\lVert U-V\right\rVert_2$ where $f_U = A\mapsto UAU^*$?

Proof of Existence of Complete Field with Dense Subfield

Definition of Compactness

Is $\{f \in \mathcal{C}[0,1]| \int_0^\frac{1}{2}f - \int_\frac{1}{2}^1 f = 1\}$ a connected set?

Assumption from Tietze's extension theorem as a sufficient condition for a set in metric space to be closed

Cantor's intersection theorem with diameters bounded below

Why is the set ${\{1\}}$ closed on $\mathbb{R}$ with the metric $d(x,y) = |x−y|$

Closure of set in set notation involving a combination of metrics

If the space $B(X,Y)$ of bounded function from $X$ into $Y$ is a complete metric space, show that $Y$ is a complete metric space.

Finite set implies sequentially compact

Are all the $\ell^p$ metrics topologically equivalent for positive integer values of $p$?

Uniform limit not being equal to pointwise limit?

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