Question

Disconnectedness of closed intervals in Sorgenfrey's line

score 324 · Answer 1 · 2018-04-28 20:21:25

324

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Disconnectedness of closed intervals in Sorgenfrey's line

Published on 28 Apr 2018 - 20:21

score 66 · Answer 2 · 2018-08-06 23:08:34

66

Views

One-Sided Notion of Topological Closure

Published on 06 Aug 2018 - 23:08

score 535 · Answer 3 · 2018-12-06 09:29:25

535

Views

Connected topologies on $\mathbb{R}$ strictly between the usual topology and the lower-limit topology

Published on 06 Dec 2018 - 9:29

score 188 · Answer 4 · 2019-01-21 11:52:35

188

Views

Lower limit topology and empty set

Published on 21 Jan 2019 - 11:52

score 224 · Answer 5 · 2019-01-27 09:58:45

224

Views

$\mathscr{B} = \{ [a, b) | a< b \in \mathbb{R} \}$ is a basis for a Topology in $\mathbb{R}$

Published on 27 Jan 2019 - 9:58

score 44 · Answer 6 · 2019-04-09 10:18:53

44

Views

Compact sets through topologies over a set

Published on 09 Apr 2019 - 10:18

score 2.4k · Answer 7 · 2026-02-22 23:29:46

2.4k

Views

How to show $R_l$ is Lindelöf space?

Published on 22 Feb 2026 - 23:29

score 720 · Answer 8 · 2019-05-10 09:42:14

720

Views

Topology Munkres ($2^\text{ed}$) $\S 16$ Exercise $2$: Subspaces of Finer Topologies

Published on 10 May 2019 - 9:42

score 75 · Answer 9 · 2019-05-26 08:11:12

75

Views

Example 2, Sec. 31, in Munkres' TOPOLOGY, 2nd ed: Normality of $\mathbb{R}_l$ --- Why are these two sets disjoint?

Published on 26 May 2019 - 8:11

score 30 · Answer 10 · 2019-09-25 05:18:54

30

Views

If $f:X\to Y$ is defined by $f(x)=1,x<0$; $f(x)=2,x\geq 0$, and $X$ and $Y$ have Sorgenfrey topology, is $f$ continuous?

Published on 25 Sep 2019 - 5:18

score 2.3k · Answer 11 · 2014-04-10 06:11:08

2.3k

Views

Is set on lower-limit topology path-connected?

Published on 10 Apr 2014 - 6:11

score 9.6k · Answer 12 · 2014-07-08 00:14:14

9.6k

Views

Is the lower limit topology finer than the standard topology on $\mathbb{R}$?

Published on 08 Jul 2014 - 0:14

score 1k · Answer 13 · 2014-10-16 07:23:12

1k

Views

Show that the Sorgenfrey line does not have a countable basis.

Published on 16 Oct 2014 - 7:23

score 374 · Answer 14 · 2014-11-27 08:05:25

374

Views

Continuity of addition under the lower limit topology

Published on 27 Nov 2014 - 8:05

score 257 · Answer 15 · 2014-11-29 02:52:22

257

Views

$\{1-\frac{1}{n} \}_n$ does not converge in the Sorgenfry line

Published on 29 Nov 2014 - 2:52

List Question

Disconnectedness of closed intervals in Sorgenfrey's line

One-Sided Notion of Topological Closure

Connected topologies on $\mathbb{R}$ strictly between the usual topology and the lower-limit topology

Lower limit topology and empty set

$\mathscr{B} = \{ [a, b) | a< b \in \mathbb{R} \}$ is a basis for a Topology in $\mathbb{R}$

Compact sets through topologies over a set

How to show $R_l$ is Lindelöf space?

Topology Munkres ($2^\text{ed}$) $\S 16$ Exercise $2$: Subspaces of Finer Topologies

Example 2, Sec. 31, in Munkres' TOPOLOGY, 2nd ed: Normality of $\mathbb{R}_l$ --- Why are these two sets disjoint?

If $f:X\to Y$ is defined by $f(x)=1,x<0$; $f(x)=2,x\geq 0$, and $X$ and $Y$ have Sorgenfrey topology, is $f$ continuous?

Is set on lower-limit topology path-connected?

Is the lower limit topology finer than the standard topology on $\mathbb{R}$?

Show that the Sorgenfrey line does not have a countable basis.

Continuity of addition under the lower limit topology

$\{1-\frac{1}{n} \}_n$ does not converge in the Sorgenfry line

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