Question

$\{1/n\}_n$ converges in the Sorgenfrey line

score 435 · Answer 1 · 2014-11-29 04:50:36

435

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$\{1/n\}_n$ converges in the Sorgenfrey line

Published on 29 Nov 2014 - 4:50

score 130 · Answer 2 · 2019-11-06 15:22:15

130

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$\epsilon - \delta$ definition of continuity

Published on 06 Nov 2019 - 15:22

score 34 · Answer 3 · 2020-02-07 15:29:58

34

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Sorgenfrey-Line, [x, ->) represented as a union of half-intervals

Published on 07 Feb 2020 - 15:29

score 464 · Answer 4 · 2020-04-01 19:43:58

464

Views

Questions about completely normal spaces.

Published on 01 Apr 2020 - 19:43

score 577 · Answer 5 · 2020-04-14 00:33:26

577

Views

Proving $R_L \times R_L$ is completely regular. Meaning $R_L \times R_L$ is an example of a space which is completely regular, but not normal

Published on 14 Apr 2020 - 0:33

score 57 · Answer 6 · 2020-05-17 20:27:58

57

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Example 4, Sec. 30, and Example 3, Sec. 31, in Munkres' TOPOLOGY, 2nd ed: How is this set closed in $\mathbb{R}_l^2$?

Published on 17 May 2020 - 20:27

score 416 · Answer 7 · 2020-05-24 18:13:49

416

Views

Lower limit topology on $\mathbb R$ is regular

Published on 24 May 2020 - 18:13

score 1.5k · Answer 8 · 2016-08-18 23:35:26

1.5k

Views

Open sets which are not closed in the Sorgenfrey line

Published on 18 Aug 2016 - 23:35

score 2.1k · Answer 9 · 2016-09-10 16:57:52

2.1k

Views

Interval $[0,1]$ is neither compact nor connected in the Sorgenfrey line.

Published on 10 Sep 2016 - 16:57

score 103 · Answer 10 · 2016-11-22 11:27:28

103

Views

Example of cont. map. $\psi: \mathbb{R}_l \to \mathbb{R}_l$ such that $ \phi: \mathbb{R}\to \mathbb{R} $, def. by $ \phi(x)=\psi(x) $, is not cont.

Published on 22 Nov 2016 - 11:27

score 1.4k · Answer 11 · 2016-11-23 09:08:53

1.4k

Views

Prove that the Sorgenfrey line is not connected

Published on 23 Nov 2016 - 9:08

score 2.5k · Answer 12 · 2016-11-23 09:30:22

2.5k

Views

Prove that the Sorgenfrey line is totally disconnected

Published on 23 Nov 2016 - 9:30

score 597 · Answer 13 · 2016-12-06 02:03:46

597

Views

Let $X=\mathbb{R}$ with the lower limit topology, and $Y=\mathbb{R}$ with the upper limit topology. Is $[1,2) \times [1,2)$ open in $X \times Y$

Published on 06 Dec 2016 - 2:03

score 2.6k · Answer 14 · 2017-01-30 18:42:11

2.6k

Views

$\mathbb{R}_\ell$ is not locally compact

Published on 30 Jan 2017 - 18:42

score 59 · Answer 15 · 2023-07-05 02:49:33

59

Views

Real line and the Sorgenfrey line have the same dense subsets

Published on 05 Jul 2023 - 2:49

List Question

$\{1/n\}_n$ converges in the Sorgenfrey line

$\epsilon - \delta$ definition of continuity

Sorgenfrey-Line, [x, ->) represented as a union of half-intervals

Questions about completely normal spaces.

Proving $R_L \times R_L$ is completely regular. Meaning $R_L \times R_L$ is an example of a space which is completely regular, but not normal

Example 4, Sec. 30, and Example 3, Sec. 31, in Munkres' TOPOLOGY, 2nd ed: How is this set closed in $\mathbb{R}_l^2$?

Lower limit topology on $\mathbb R$ is regular

Open sets which are not closed in the Sorgenfrey line

Interval $[0,1]$ is neither compact nor connected in the Sorgenfrey line.

Example of cont. map. $\psi: \mathbb{R}_l \to \mathbb{R}_l$ such that $ \phi: \mathbb{R}\to \mathbb{R} $, def. by $ \phi(x)=\psi(x) $, is not cont.

Prove that the Sorgenfrey line is not connected

Prove that the Sorgenfrey line is totally disconnected

Let $X=\mathbb{R}$ with the lower limit topology, and $Y=\mathbb{R}$ with the upper limit topology. Is $[1,2) \times [1,2)$ open in $X \times Y$

$\mathbb{R}_\ell$ is not locally compact

Real line and the Sorgenfrey line have the same dense subsets

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