Question

Prove $E \subset X$ is not connected (definition: $Cl(A) \cup B = A \cap Cl(B) = \emptyset$) iff there exists open sets

score 259 · Answer 1 · 2026-04-15 05:19:47

259

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Prove $E \subset X$ is not connected (definition: $Cl(A) \cup B = A \cap Cl(B) = \emptyset$) iff there exists open sets

Published on 15 Apr 2026 - 5:19

score 67 · Answer 2 · 2026-04-12 08:36:29

67

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Proposition 7.2. of Adkins' Algebra

Published on 12 Apr 2026 - 8:36

score 127 · Answer 3 · 2026-04-15 16:44:27

127

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Left inverse proof

Published on 15 Apr 2026 - 16:44

score 5.3k · Answer 4 · 2026-05-01 18:58:46

5.3k

Views

Difference between $\square $ and $\blacksquare $

Published on 01 May 2026 - 18:58

score 8.2k · Answer 5 · 2026-04-17 03:45:41

8.2k

Views

prove that if x is a real number, then $\lfloor2x\rfloor=\lfloor x\rfloor+\lfloor x + \frac{1}{2}\rfloor$

Published on 17 Apr 2026 - 3:45

score 2k · Answer 6 · 2026-04-16 00:24:07

2k

Views

If $f$ is differentiable on a closed bounded interval, is $f$ bounded?

Published on 16 Apr 2026 - 0:24

score 1.6k · Answer 7 · 2026-04-16 08:25:02

1.6k

Views

A or B must be an irrational number proof

Published on 16 Apr 2026 - 8:25

score 777 · Answer 8 · 2026-04-13 20:52:56

777

Views

A sequence that is uniformly bounded on a compact interval is equicontinuous

Published on 13 Apr 2026 - 20:52

score 64 · Answer 9 · 2026-04-15 05:54:06

64

Views

How to prove that $f: \mathbb{N}^2 \to \mathbb{N}$ is a bijection?

Published on 15 Apr 2026 - 5:54

score 183 · Answer 10 · 2026-04-10 21:39:32

183

Views

About theorems on nowhere dense set

Published on 10 Apr 2026 - 21:39

score 2.6k · Answer 11 · 2026-04-14 06:22:18

2.6k

Views

$AA^T$ invertible or not?

Published on 14 Apr 2026 - 6:22

score 260 · Answer 12 · 2026-04-16 00:59:37

260

Views

Why is this corollary of Liouville true

Published on 16 Apr 2026 - 0:59

score 232 · Answer 13 · 2026-04-17 00:49:30

232

Views

Suppose that both $A$ and $B$ have a left inverse. Show that $AB$ has a left inverse.

Published on 17 Apr 2026 - 0:49

score 619 · Answer 14 · 2026-04-14 21:18:57

619

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$n_1,...,n_k$ pair coprime $\!\iff\! {\rm lcm}(n_1,...,n_k)=n_1...n_k$ [lcm = product for coprimes]

Published on 14 Apr 2026 - 21:18

score 66 · Answer 15 · 2026-04-16 14:26:58

66

Views

If we let $A$ be an $m × n$ matrix. Suppose that the rows of $A$ are linearly independent.

Published on 16 Apr 2026 - 14:26

List Question

Prove $E \subset X$ is not connected (definition: $Cl(A) \cup B = A \cap Cl(B) = \emptyset$) iff there exists open sets

Proposition 7.2. of Adkins' Algebra

Left inverse proof

Difference between $\square $ and $\blacksquare $

prove that if x is a real number, then $\lfloor2x\rfloor=\lfloor x\rfloor+\lfloor x + \frac{1}{2}\rfloor$

If $f$ is differentiable on a closed bounded interval, is $f$ bounded?

A or B must be an irrational number proof

A sequence that is uniformly bounded on a compact interval is equicontinuous

How to prove that $f: \mathbb{N}^2 \to \mathbb{N}$ is a bijection?

About theorems on nowhere dense set

$AA^T$ invertible or not?

Why is this corollary of Liouville true

Suppose that both $A$ and $B$ have a left inverse. Show that $AB$ has a left inverse.

$n_1,...,n_k$ pair coprime $\!\iff\! {\rm lcm}(n_1,...,n_k)=n_1...n_k$ [lcm = product for coprimes]

If we let $A$ be an $m × n$ matrix. Suppose that the rows of $A$ are linearly independent.

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