Question

Why do we require $K$ to be compact instead of just finite in $(X=\mathbb{R} \cup \{P\}, \tau_2=\tau_e \cup \{X\setminus K\})$ for compactness?

score 45 · Answer 1 · 2020-07-13 15:04:57

45

Views

Why do we require $K$ to be compact instead of just finite in $(X=\mathbb{R} \cup \{P\}, \tau_2=\tau_e \cup \{X\setminus K\})$ for compactness?

Published on 13 Jul 2020 - 15:04

score 153 · Answer 2 · 2020-07-13 20:43:07

153

Views

About the one point compactification

Published on 13 Jul 2020 - 20:43

score 75 · Answer 3 · 2020-07-14 14:42:13

75

Views

confused about quotienting $\Bbb R^2$ by $\Bbb Z^2$ vs. compactifying $ \Bbb R^2$ first and then gluing sides

Published on 14 Jul 2020 - 14:42

score 35 · Answer 4 · 2020-07-29 18:14:05

35

Views

Point compactification of $\mathbb{R}^2$ into $\mathbb{S}^2$

Published on 29 Jul 2020 - 18:14

score 90 · Answer 5 · 2016-08-02 19:34:09

90

Views

$\pm\infty$ versus neutral $\infty$ in extensions (compactifications) of $\mathbb R$

Published on 02 Aug 2016 - 19:34

score 211 · Answer 6 · 2016-08-08 17:44:35

211

Views

Does the function $f(x)=x^2$ admit a continuous extension to the Stone-Cech compactification?

Published on 08 Aug 2016 - 17:44

score 707 · Answer 7 · 2016-08-09 01:00:40

707

Views

What does the 1-point compactification of disjoint open intervals look like?

Published on 09 Aug 2016 - 1:00

score 4.2k · Answer 8 · 2016-08-09 08:15:41

4.2k

Views

Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff

Published on 09 Aug 2016 - 8:15

score 671 · Answer 9 · 2016-08-11 05:15:51

671

Views

Show that every locally compact Hausdorff space is embedded in a compact Hausdorff space

Published on 11 Aug 2016 - 5:15

score 207 · Answer 10 · 2016-08-11 11:18:47

207

Views

One point compatification of $(-1,0)\cup (0,1)$

Published on 11 Aug 2016 - 11:18

score 314 · Answer 11 · 2016-08-12 05:05:27

314

Views

How to visualize the one point compactification of a plane with finitely points removed and $\mathbb{R}_{\text{discrete}}$

Published on 12 Aug 2016 - 5:05

score 1.9k · Answer 12 · 2016-08-15 02:22:58

1.9k

Views

Show that the Stone–Čech compactification $\beta \mathbb{Z}$ is not metrizable.

Published on 15 Aug 2016 - 2:22

score 108 · Answer 13 · 2016-08-31 07:07:39

108

Views

Stone-Cech extension of a function satisfying $f(x+y)=f(x)+f(y)$?

Published on 31 Aug 2016 - 7:07

score 204 · Answer 14 · 2016-09-08 00:08:55

204

Views

How can I find the presentation of the compactification of a planar hyperelliptic curve?

Published on 08 Sep 2016 - 0:08

score 83 · Answer 15 · 2016-11-01 01:31:12

83

Views

General Stone-Čech compactification from the discrete case

Published on 01 Nov 2016 - 1:31

List Question

Why do we require $K$ to be compact instead of just finite in $(X=\mathbb{R} \cup \{P\}, \tau_2=\tau_e \cup \{X\setminus K\})$ for compactness?

About the one point compactification

confused about quotienting $\Bbb R^2$ by $\Bbb Z^2$ vs. compactifying $ \Bbb R^2$ first and then gluing sides

Point compactification of $\mathbb{R}^2$ into $\mathbb{S}^2$

$\pm\infty$ versus neutral $\infty$ in extensions (compactifications) of $\mathbb R$

Does the function $f(x)=x^2$ admit a continuous extension to the Stone-Cech compactification?

What does the 1-point compactification of disjoint open intervals look like?

Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff

Show that every locally compact Hausdorff space is embedded in a compact Hausdorff space

One point compatification of $(-1,0)\cup (0,1)$

How to visualize the one point compactification of a plane with finitely points removed and $\mathbb{R}_{\text{discrete}}$

Show that the Stone–Čech compactification $\beta \mathbb{Z}$ is not metrizable.

Stone-Cech extension of a function satisfying $f(x+y)=f(x)+f(y)$?

How can I find the presentation of the compactification of a planar hyperelliptic curve?

General Stone-Čech compactification from the discrete case

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