Question

If $\{q_\alpha: X_\alpha \to Y_\alpha\}$ is a family of quotient maps, then $q:\coprod_\alpha X_\alpha \to \coprod_\alpha Y_\alpha$ is a quotient map.

score 503 · Answer 1 · 2026-03-25 04:59:33

503

Views

If $\{q_\alpha: X_\alpha \to Y_\alpha\}$ is a family of quotient maps, then $q:\coprod_\alpha X_\alpha \to \coprod_\alpha Y_\alpha$ is a quotient map.

Published on 25 Mar 2026 - 4:59

score 100 · Answer 2 · 2018-06-04 19:37:51

100

Views

Proof for: $x \in \overline{A} \iff (x_n)_n$ exists in $A$ with $x_n \to x$

Published on 04 Jun 2018 - 19:37

score 259 · Answer 3 · 2018-06-04 21:07:49

259

Views

Properly discontinuous action in metric spaces

Published on 04 Jun 2018 - 21:07

score 161 · Answer 4 · 2026-03-28 14:53:44

161

Views

Countably compact if and only if countable closed sets are compact

Published on 28 Mar 2026 - 14:53

score 40 · Answer 5 · 2018-06-04 22:52:22

40

Views

Open Set Clarification: Sequence Definition

Published on 04 Jun 2018 - 22:52

score 116 · Answer 6 · 2026-04-01 20:03:08

116

Views

Show that the barycentric coordinates $t_o(x), t_1(x),...,t_n(x)$ continually depend on $x$.

Published on 01 Apr 2026 - 20:03

score 7k · Answer 7 · 2026-03-26 04:50:53

7k

Views

Example of a metric space first countable but not second countable.

Published on 26 Mar 2026 - 4:50

score 67 · Answer 8 · 2026-03-30 00:04:11

67

Views

Let $W=[0,1]\times[0,1]$, where $(0,y)\sim(1,1-y)$ for all $0\leq y\leq 1$. Calculate the homology groups of $W$

Published on 30 Mar 2026 - 0:04

score 44 · Answer 9 · 2026-03-29 06:55:37

44

Views

existence of finite-dimensional subspace containing a sequence

Published on 29 Mar 2026 - 6:55

score 155 · Answer 10 · 2026-03-25 03:22:50

155

Views

Condition that the faces of a graph be unique?

Published on 25 Mar 2026 - 3:22

score 226 · Answer 11 · 2026-03-30 01:53:07

226

Views

Using Mayer-Vietoris to compute Homology

Published on 30 Mar 2026 - 1:53

score 35 · Answer 12 · 2026-04-03 14:07:19

35

Views

Stuck on a proof by Skylarenko lemma 1

Published on 03 Apr 2026 - 14:07

score 624 · Answer 13 · 2026-04-01 20:01:08

624

Views

Is there a continuous surjective map of $\mathbb{R}$ onto $\mathbb{R}^{\infty}$?

Published on 01 Apr 2026 - 20:01

score 73 · Answer 14 · 2026-04-01 20:00:38

73

Views

is there any contractable space with three points?

Published on 01 Apr 2026 - 20:00

score 97 · Answer 15 · 2026-04-01 21:33:38

97

Views

Prove a quotient space which consistis of 2 discs is simply connected.

Published on 01 Apr 2026 - 21:33

List Question

If $\{q_\alpha: X_\alpha \to Y_\alpha\}$ is a family of quotient maps, then $q:\coprod_\alpha X_\alpha \to \coprod_\alpha Y_\alpha$ is a quotient map.

Proof for: $x \in \overline{A} \iff (x_n)_n$ exists in $A$ with $x_n \to x$

Properly discontinuous action in metric spaces

Countably compact if and only if countable closed sets are compact

Open Set Clarification: Sequence Definition

Show that the barycentric coordinates $t_o(x), t_1(x),...,t_n(x)$ continually depend on $x$.

Example of a metric space first countable but not second countable.

Let $W=[0,1]\times[0,1]$, where $(0,y)\sim(1,1-y)$ for all $0\leq y\leq 1$. Calculate the homology groups of $W$

existence of finite-dimensional subspace containing a sequence

Condition that the faces of a graph be unique?

Using Mayer-Vietoris to compute Homology

Stuck on a proof by Skylarenko lemma 1

Is there a continuous surjective map of $\mathbb{R}$ onto $\mathbb{R}^{\infty}$?

is there any contractable space with three points?

Prove a quotient space which consistis of 2 discs is simply connected.

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