Question

Continuous function from $\mathbb{R}$ standard topology to $\mathbb{R}_l$ lower limit topology

score 1k · Answer 1 · 2020-08-11 00:57:20

1k

Views

Continuous function from $\mathbb{R}$ standard topology to $\mathbb{R}_l$ lower limit topology

Published on 11 Aug 2020 - 0:57

score 133 · Answer 2 · 2020-09-11 06:56:01

133

Views

Topologies on $\mathbb{R}$

Published on 11 Sep 2020 - 6:56

score 395 · Answer 3 · 2020-10-02 06:25:01

395

Views

The Sorgenfrey plane and the Niemytzki plane are Baire spaces

Published on 02 Oct 2020 - 6:25

score 37 · Answer 4 · 2020-11-05 00:13:47

37

Views

IVT-related Topology question

Published on 05 Nov 2020 - 0:13

score 93 · Answer 5 · 2020-11-06 01:51:35

93

Views

Examples of topologies in which all open sets are countable union of base elements, but the topology itself doesn't have countable bases.

Published on 06 Nov 2020 - 1:51

score 315 · Answer 6 · 2020-11-15 22:38:31

315

Views

Prove that a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous in lower and upper limit topologies is constant.

Published on 15 Nov 2020 - 22:38

score 51 · Answer 7 · 2020-12-08 01:09:30

51

Views

Quotient map from Sorgenfrey plane to Real Line

Published on 08 Dec 2020 - 1:09

score 108 · Answer 8 · 2021-01-01 18:42:00

108

Views

Are $[0, 1)$ and $[0, 1]$ homeomorphic subspaces of the Sorgenfrey line?

Published on 01 Jan 2021 - 18:42

score 62 · Answer 9 · 2021-01-04 19:07:20

62

Views

Show each interval (a,b) is open in the basis B

Published on 04 Jan 2021 - 19:07

score 612 · Answer 10 · 2021-01-13 06:56:07

612

Views

Why is the Sorgenfrey Line not second countable?

Published on 13 Jan 2021 - 6:56

score 125 · Answer 11 · 2021-02-17 00:37:45

125

Views

If f: $\mathbb{R}_{l} \rightarrow S_{\Omega}$ is continuous, then f is not injective.

Published on 17 Feb 2021 - 0:37

score 127 · Answer 12 · 2021-04-11 18:05:40

127

Views

Is the set {$1-\frac{1}{n} | n\in \mathbb N$} U {1} compact under Sorgenfrey?

Published on 11 Apr 2021 - 18:05

score 31 · Answer 13 · 2021-05-03 13:41:22

31

Views

Verifying if it is a legitimate basis for a topology

Published on 03 May 2021 - 13:41

score 313 · Answer 14 · 2021-05-30 03:37:28

313

Views

Why is the topology on the Sorgenfrey line not second countable?

Published on 30 May 2021 - 3:37

score 93 · Answer 15 · 2026-02-23 06:56:55

93

Views

Proof Verification: $\mathbb{R}_l$ is Lindelöf.

Published on 23 Feb 2026 - 6:56

List Question

Continuous function from $\mathbb{R}$ standard topology to $\mathbb{R}_l$ lower limit topology

Topologies on $\mathbb{R}$

The Sorgenfrey plane and the Niemytzki plane are Baire spaces

IVT-related Topology question

Examples of topologies in which all open sets are countable union of base elements, but the topology itself doesn't have countable bases.

Prove that a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous in lower and upper limit topologies is constant.

Quotient map from Sorgenfrey plane to Real Line

Are $[0, 1)$ and $[0, 1]$ homeomorphic subspaces of the Sorgenfrey line?

Show each interval (a,b) is open in the basis B

Why is the Sorgenfrey Line not second countable?

If f: $\mathbb{R}_{l} \rightarrow S_{\Omega}$ is continuous, then f is not injective.

Is the set {$1-\frac{1}{n} | n\in \mathbb N$} U {1} compact under Sorgenfrey?

Verifying if it is a legitimate basis for a topology

Why is the topology on the Sorgenfrey line not second countable?

Proof Verification: $\mathbb{R}_l$ is Lindelöf.

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