Question

Let $f:A→B$ and $g:B→C$ be maps. Prove that if $g∘f$ is one to one and f is surjection, then g is one to one.

score 308 · Answer 1 · 2026-04-15 16:46:20

308

Views

Let $f:A→B$ and $g:B→C$ be maps. Prove that if $g∘f$ is one to one and f is surjection, then g is one to one.

Published on 15 Apr 2026 - 16:46

score 35 · Answer 2 · 2026-04-16 15:20:38

35

Views

Let B be any set and $g : B \rightarrow B$ be a function satisfying the condition $(g \circ g)(x) = x$

Published on 16 Apr 2026 - 15:20

score 765 · Answer 3 · 2026-04-16 11:17:49

765

Views

Let $f,g: X \rightarrow Y$ be continuous and $Y$ be Hausdorff. Prove that $\{x | f(x) = g(x)\}$ is a closed subset of $X$.

Published on 16 Apr 2026 - 11:17

score 93 · Answer 4 · 2026-05-10 15:24:02

93

Views

$1/(51 +u^2) + 1/(51 +v^2) + 1/(51 +w^2)$ inequality

Published on 10 May 2026 - 15:24

score 8.3k · Answer 5 · 2026-04-16 12:01:48

8.3k

Views

Prove that if a sequence $x_n$ tends to infinity, then $\frac{1}{x_n}$ converges to zero.

Published on 16 Apr 2026 - 12:01

score 126 · Answer 6 · 2026-05-10 17:12:44

126

Views

Is $\mathbb{Z}[\sqrt{-5},1/10]$ a PID

Published on 10 May 2026 - 17:12

score 531 · Answer 7 · 2026-04-16 20:12:20

531

Views

Two disjoint closed sets $A,B$ with $B$ compact, show $d(A,B) > 0$ Verify my proof

Published on 16 Apr 2026 - 20:12

score 76 · Answer 8 · 2026-04-12 00:38:37

76

Views

Proof of a ring property

Published on 12 Apr 2026 - 0:38

score 30 · Answer 9 · 2026-05-02 10:19:15

30

Views

Property of absolute continuity of measures and finite variation

Published on 02 May 2026 - 10:19

score 114 · Answer 10 · 2026-05-10 10:56:19

114

Views

Why are these angles equal?

Published on 10 May 2026 - 10:56

score 955 · Answer 11 · 2026-04-15 08:48:57

955

Views

Proving $\frac{S_n}{n^{1/p}} \to 0$ almost surely implies $E|X_i|^p < \infty$

Published on 15 Apr 2026 - 8:48

score 57 · Answer 12 · 2026-04-10 00:08:58

57

Views

Proving plane geometry problem

Published on 10 Apr 2026 - 0:08

score 219 · Answer 13 · 2026-04-16 18:37:46

219

Views

Are continuous functions on a closed interval nowhere infinite?

Published on 16 Apr 2026 - 18:37

score 240 · Answer 14 · 2026-04-15 10:33:17

Let S be a non-empty bounded set, and let $a,b \in \mathbb{R}$. Define $T = \{a \cdot s + b | s \in S\}$. Find a formula for Sup($T$).

score 33 · Answer 15 · 2026-04-16 02:58:05

33

Views

Correspondence between $(\mathbb{R}P^2,q) \rightarrow (S^1 \times S^1, x_0)$ and $(\mathbb{R}P^2,q) \rightarrow (\mathbb{R}^2,(0,0))$

Published on 16 Apr 2026 - 2:58

List Question

Let $f:A→B$ and $g:B→C$ be maps. Prove that if $g∘f$ is one to one and f is surjection, then g is one to one.

Let B be any set and $g : B \rightarrow B$ be a function satisfying the condition $(g \circ g)(x) = x$

Let $f,g: X \rightarrow Y$ be continuous and $Y$ be Hausdorff. Prove that $\{x | f(x) = g(x)\}$ is a closed subset of $X$.

$1/(51 +u^2) + 1/(51 +v^2) + 1/(51 +w^2)$ inequality

Prove that if a sequence $x_n$ tends to infinity, then $\frac{1}{x_n}$ converges to zero.

Is $\mathbb{Z}[\sqrt{-5},1/10]$ a PID

Two disjoint closed sets $A,B$ with $B$ compact, show $d(A,B) > 0$ Verify my proof

Proof of a ring property

Property of absolute continuity of measures and finite variation

Why are these angles equal?

Proving $\frac{S_n}{n^{1/p}} \to 0$ almost surely implies $E|X_i|^p < \infty$

Proving plane geometry problem

Are continuous functions on a closed interval nowhere infinite?

Let S be a non-empty bounded set, and let $a,b \in \mathbb{R}$. Define $T = \{a \cdot s + b | s \in S\}$. Find a formula for Sup($T$).

Correspondence between $(\mathbb{R}P^2,q) \rightarrow (S^1 \times S^1, x_0)$ and $(\mathbb{R}P^2,q) \rightarrow (\mathbb{R}^2,(0,0))$

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