Question

Is the inverse of bijective continuous functions always continuous?

score 720 · Answer 1 · 2026-05-10 19:35:52

720

Views

Is the inverse of bijective continuous functions always continuous?

Published on 10 May 2026 - 19:35

score 248 · Answer 2 · 2026-05-13 21:26:20

248

Views

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

Published on 13 May 2026 - 21:26

score 65 · Answer 3 · 2026-05-10 19:35:27

65

Views

Motivation behind proof of Metrizability & local countable basis equivalence

Published on 10 May 2026 - 19:35

score 81 · Answer 4 · 2026-05-11 05:26:49

81

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 11 May 2026 - 5:26

score 185 · Answer 5 · 2026-05-10 13:50:37

185

Views

Proof of Existence of Complete Field with Dense Subfield

Published on 10 May 2026 - 13:50

score 312 · Answer 6 · 2026-05-14 00:07:51

312

Views

Definition of Compactness

Published on 14 May 2026 - 0:07

score 57 · Answer 7 · 2026-04-17 15:42:14

57

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 17 Apr 2026 - 15:42

score 295 · Answer 8 · 2026-04-13 01:05:58

295

Views

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

Published on 13 Apr 2026 - 1:05

score 406 · Answer 9 · 2026-04-13 08:17:26

406

Views

Cantor's intersection theorem with diameters bounded below

Published on 13 Apr 2026 - 8:17

score 90 · Answer 10 · 2026-04-15 22:58:53

90

Views

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

Published on 15 Apr 2026 - 22:58

score 35 · Answer 11 · 2026-04-13 19:23:33

35

Views

Closure of set in set notation involving a combination of metrics

Published on 13 Apr 2026 - 19:23

score 92 · Answer 12 · 2026-04-14 13:00:00

92

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 14 Apr 2026 - 13:00

score 983 · Answer 13 · 2026-05-13 23:37:54

983

Views

Finite set implies sequentially compact

Published on 13 May 2026 - 23:37

score 1.1k · Answer 14 · 2026-04-17 04:18:27

1.1k

Views

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

Published on 17 Apr 2026 - 4:18

score 393 · Answer 15 · 2026-05-10 15:45:20

393

Views

Uniform limit not being equal to pointwise limit?

Published on 10 May 2026 - 15:45

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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