Question

Disconnectedness of closed intervals in Sorgenfrey's line

score 325 · Answer 1 · 2026-02-23 01:21:42

325

Views

Disconnectedness of closed intervals in Sorgenfrey's line

Published on 23 Feb 2026 - 1:21

score 67 · Answer 2 · 2026-02-23 01:20:48

67

Views

One-Sided Notion of Topological Closure

Published on 23 Feb 2026 - 1:20

score 536 · Answer 3 · 2026-02-23 01:21:42

536

Views

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

Published on 23 Feb 2026 - 1:21

score 189 · Answer 4 · 2026-02-23 01:19:25

189

Views

Lower limit topology and empty set

Published on 23 Feb 2026 - 1:19

score 225 · Answer 5 · 2026-02-23 01:20:46

225

Views

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

Published on 23 Feb 2026 - 1:20

score 45 · Answer 6 · 2026-02-23 01:17:54

45

Views

Compact sets through topologies over a set

Published on 23 Feb 2026 - 1:17

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 721 · Answer 8 · 2026-02-23 01:21:41

721

Views

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

Published on 23 Feb 2026 - 1:21

score 76 · Answer 9 · 2026-02-23 01:22:12

76

Views

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

Published on 23 Feb 2026 - 1:22

score 31 · Answer 10 · 2026-02-23 01:23:46

31

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 23 Feb 2026 - 1:23

score 2.3k · Answer 11 · 2026-02-23 01:18:53

2.3k

Views

Is set on lower-limit topology path-connected?

Published on 23 Feb 2026 - 1:18

score 9.6k · Answer 12 · 2026-02-23 02:59:19

9.6k

Views

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

Published on 23 Feb 2026 - 2:59

score 1k · Answer 13 · 2026-02-23 02:55:23

1k

Views

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

Published on 23 Feb 2026 - 2:55

score 375 · Answer 14 · 2026-02-23 02:57:41

375

Views

Continuity of addition under the lower limit topology

Published on 23 Feb 2026 - 2:57

score 258 · Answer 15 · 2026-02-23 02:59:19

258

Views

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

Published on 23 Feb 2026 - 2:59

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

Trending Questions

Popular # Hahtags

Popular Questions