Question

Prove that $C$ is open with respect to $A\cup B$ if $C\subset A\cap B$, $C$ is open with respect to $A$ and $C$ is open with respect to $B$.

score 115 · Answer 1 · 2019-12-30 23:22:50

Prove that $C$ is open with respect to $A\cup B$ if $C\subset A\cap B$, $C$ is open with respect to $A$ and $C$ is open with respect to $B$.

score 131 · Answer 2 · 2019-12-31 01:02:55

131

Views

$\{ b_i + v \}$ is a basis for $V$ if $v = \sum \alpha_i b_i$ such that $\sum \alpha_i \neq -1$

Published on 31 Dec 2019 - 1:02

score 137 · Answer 3 · 2019-12-31 03:41:17

137

Views

Proving Specker's Theorem (Set Theory)

Published on 31 Dec 2019 - 3:41

score 160 · Answer 4 · 2026-03-28 15:11:24

160

Views

Proving that only entire cusp form of weight k < 12 is zero function.

Published on 28 Mar 2026 - 15:11

score 421 · Answer 5 · 2019-12-31 13:27:36

421

Views

High school contest math problem

Published on 31 Dec 2019 - 13:27

score 189 · Answer 6 · 2026-03-30 03:05:32

189

Views

Product space and Basis

Published on 30 Mar 2026 - 3:05

score 447 · Answer 7 · 2026-03-26 22:15:18

447

Views

Proof verification: Does $\alpha$-Hölder condition on an open interval imply its uniform continuity and $f$ is constant when $\alpha>1$?

Published on 26 Mar 2026 - 22:15

score 114 · Answer 8 · 2019-12-31 18:17:08

114

Views

Proof of $f(x):=|x|^p \text{ differentiable in } 0 \Leftrightarrow p>1$

Published on 31 Dec 2019 - 18:17

score 143 · Answer 9 · 2019-12-31 19:26:41

143

Views

Rudin exercise 1.5: rigorously reasoning from $A$ to $-A$

Published on 31 Dec 2019 - 19:26

score 1.2k · Answer 10 · 2019-12-31 19:55:18

1.2k

Views

Give an example of a linear map $T$ such that $\dim(\operatorname{null}T) = 3$ and $\dim(\operatorname{range}T) = 2$

Published on 31 Dec 2019 - 19:55

score 91 · Answer 11 · 2019-12-31 21:39:49

91

Views

Find the possible values of $\dim( U \cap W)$

Published on 31 Dec 2019 - 21:39

score 3.1k · Answer 12 · 2020-01-01 01:14:22

3.1k

Views

Counting for possibilities of passwords containing at least one uppercase letter, one lowercase letter, and one digit

Published on 01 Jan 2020 - 1:14

score 982 · Answer 13 · 2020-01-01 11:01:44

982

Views

$|A| = |B|$ Show that this function is surjective when it is one to one

Published on 01 Jan 2020 - 11:01

score 100 · Answer 14 · 2020-01-01 14:07:36

100

Views

Proof verification (sets & logic)

Published on 01 Jan 2020 - 14:07

score 40 · Answer 15 · 2020-01-01 15:19:55

40

Views

Cardinality of $\operatorname{Hom}_{K\text{-alg}}(A,L),$ where $A$ is a finite dim. $K$-alg, $L/K$ a field extension

Published on 01 Jan 2020 - 15:19

List Question

Prove that $C$ is open with respect to $A\cup B$ if $C\subset A\cap B$, $C$ is open with respect to $A$ and $C$ is open with respect to $B$.

$\{ b_i + v \}$ is a basis for $V$ if $v = \sum \alpha_i b_i$ such that $\sum \alpha_i \neq -1$

Proving Specker's Theorem (Set Theory)

Proving that only entire cusp form of weight k < 12 is zero function.

High school contest math problem

Product space and Basis

Proof verification: Does $\alpha$-Hölder condition on an open interval imply its uniform continuity and $f$ is constant when $\alpha>1$?

Proof of $f(x):=|x|^p \text{ differentiable in } 0 \Leftrightarrow p>1$

Rudin exercise 1.5: rigorously reasoning from $A$ to $-A$

Give an example of a linear map $T$ such that $\dim(\operatorname{null}T) = 3$ and $\dim(\operatorname{range}T) = 2$

Find the possible values of $\dim( U \cap W)$

Counting for possibilities of passwords containing at least one uppercase letter, one lowercase letter, and one digit

$|A| = |B|$ Show that this function is surjective when it is one to one

Proof verification (sets & logic)

Cardinality of $\operatorname{Hom}_{K\text{-alg}}(A,L),$ where $A$ is a finite dim. $K$-alg, $L/K$ a field extension

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