Question

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

score 436 · Answer 1 · 2026-02-23 04:59:07

436

Views

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

Published on 23 Feb 2026 - 4:59

score 132 · Answer 2 · 2026-04-01 17:52:18

132

Views

$\epsilon - \delta$ definition of continuity

Published on 01 Apr 2026 - 17:52

score 35 · Answer 3 · 2026-02-23 04:56:33

35

Views

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

Published on 23 Feb 2026 - 4:56

score 466 · Answer 4 · 2026-04-01 10:43:08

466

Views

Questions about completely normal spaces.

Published on 01 Apr 2026 - 10:43

score 578 · Answer 5 · 2026-02-23 04:59:34

578

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 23 Feb 2026 - 4:59

score 58 · Answer 6 · 2026-02-23 04:59:07

58

Views

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 23 Feb 2026 - 4:59

score 417 · Answer 7 · 2026-02-23 04:53:25

417

Views

Lower limit topology on $\mathbb R$ is regular

Published on 23 Feb 2026 - 4:53

score 1.5k · Answer 8 · 2026-02-23 04:55:27

1.5k

Views

Open sets which are not closed in the Sorgenfrey line

Published on 23 Feb 2026 - 4:55

score 2.1k · Answer 9 · 2026-02-23 04:56:24

2.1k

Views

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

Published on 23 Feb 2026 - 4:56

score 104 · Answer 10 · 2026-02-23 04:56:33

104

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 23 Feb 2026 - 4:56

score 1.4k · Answer 11 · 2026-02-23 04:55:14

1.4k

Views

Prove that the Sorgenfrey line is not connected

Published on 23 Feb 2026 - 4:55

score 2.5k · Answer 12 · 2026-02-23 04:59:05

2.5k

Views

Prove that the Sorgenfrey line is totally disconnected

Published on 23 Feb 2026 - 4:59

score 598 · Answer 13 · 2026-02-23 04:58:24

598

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 23 Feb 2026 - 4:58

score 2.6k · Answer 14 · 2026-02-23 04:50:16

2.6k

Views

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

Published on 23 Feb 2026 - 4:50

score 60 · Answer 15 · 2026-02-23 04:55:27

60

Views

Real line and the Sorgenfrey line have the same dense subsets

Published on 23 Feb 2026 - 4:55

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

Trending Questions

Popular # Hahtags

Popular Questions