Question

Why is a set being compact equivalent to it being closed?

score 101 · Answer 1 · 2026-04-13 12:01:23

101

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Why is a set being compact equivalent to it being closed?

Published on 13 Apr 2026 - 12:01

score 95 · Answer 2 · 2026-04-12 21:50:24

95

Views

Show that the set of points at which a function is bounded is open

Published on 12 Apr 2026 - 21:50

score 264 · Answer 3 · 2026-04-14 18:58:42

264

Views

Product metric, continuity of functions and minimum

Published on 14 Apr 2026 - 18:58

score 429 · Answer 4 · 2026-04-13 12:00:10

429

Views

Higher dimensional equivalent of complex numbers

Published on 13 Apr 2026 - 12:00

score 74 · Answer 5 · 2026-04-11 14:50:36

74

Views

Is "bounded" required for the definition below

Published on 11 Apr 2026 - 14:50

score 141 · Answer 6 · 2026-04-16 14:31:03

141

Views

Prove that $f(\limsup A_n)\subset \limsup f(A_n)$.

Published on 16 Apr 2026 - 14:31

score 62 · Answer 7 · 2026-04-11 03:56:24

62

Views

Equivalence of convergence. In particular $L^p$ and in measure.

Published on 11 Apr 2026 - 3:56

score 48 · Answer 8 · 2026-04-15 23:36:11

Verify: If $0<\alpha<1$, $0\leq \beta$, then there exists $M(\alpha,\beta)>0$ so that $z^\beta e^{-z}\leq Me^{-\alpha z}$ for all $z\geq 0$

score 653 · Answer 9 · 2026-04-13 17:26:09

653

Views

Is the area the integral of the perimeter?

Published on 13 Apr 2026 - 17:26

score 414 · Answer 10 · 2026-04-12 00:01:31

414

Views

Proof of the Weierstrass M-Test

Published on 12 Apr 2026 - 0:01

score 113 · Answer 11 · 2026-04-15 07:53:43

113

Views

The Hölder condition with the negative exponent $|f(x) - f(y)| \leq \frac{1}{|x-y|}$

Published on 15 Apr 2026 - 7:53

score 185 · Answer 12 · 2026-05-04 03:59:01

185

Views

Density of n-th Power of Rationals in $\mathbb{Q}$

Published on 04 May 2026 - 3:59

score 46 · Answer 13 · 2026-04-13 14:11:29

46

Views

What does it mean to be conformal?

Published on 13 Apr 2026 - 14:11

score 95 · Answer 14 · 2026-04-13 11:47:13

95

Views

A problem about $\epsilon-\delta$ definition of a limit where the target is to find $\delta$

Published on 13 Apr 2026 - 11:47

score 508 · Answer 15 · 2026-04-29 17:52:22

508

Views

Let $a = \liminf x_n$, $b = \limsup x_n$. If $\lim (x_{n+1} - x_n) = 0$ then every element of $(a,b)$ is a subsequential limit of $(x_n)$

Published on 29 Apr 2026 - 17:52

List Question

Why is a set being compact equivalent to it being closed?

Show that the set of points at which a function is bounded is open

Product metric, continuity of functions and minimum

Higher dimensional equivalent of complex numbers

Is "bounded" required for the definition below

Prove that $f(\limsup A_n)\subset \limsup f(A_n)$.

Equivalence of convergence. In particular $L^p$ and in measure.

Verify: If $0<\alpha<1$, $0\leq \beta$, then there exists $M(\alpha,\beta)>0$ so that $z^\beta e^{-z}\leq Me^{-\alpha z}$ for all $z\geq 0$

Is the area the integral of the perimeter?

Proof of the Weierstrass M-Test

The Hölder condition with the negative exponent $|f(x) - f(y)| \leq \frac{1}{|x-y|}$

Density of n-th Power of Rationals in $\mathbb{Q}$

What does it mean to be conformal?

A problem about $\epsilon-\delta$ definition of a limit where the target is to find $\delta$

Let $a = \liminf x_n$, $b = \limsup x_n$. If $\lim (x_{n+1} - x_n) = 0$ then every element of $(a,b)$ is a subsequential limit of $(x_n)$

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