Question

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

score 1k · Answer 1 · 2026-02-23 10:16:45

1k

Views

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

Published on 23 Feb 2026 - 10:16

score 134 · Answer 2 · 2026-02-23 10:14:20

134

Views

Topologies on $\mathbb{R}$

Published on 23 Feb 2026 - 10:14

score 396 · Answer 3 · 2026-02-23 10:20:45

396

Views

The Sorgenfrey plane and the Niemytzki plane are Baire spaces

Published on 23 Feb 2026 - 10:20

score 38 · Answer 4 · 2026-02-23 10:16:52

38

Views

IVT-related Topology question

Published on 23 Feb 2026 - 10:16

score 94 · Answer 5 · 2026-02-23 10:21:50

94

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 23 Feb 2026 - 10:21

score 316 · Answer 6 · 2026-02-23 10:18:47

316

Views

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

Published on 23 Feb 2026 - 10:18

score 52 · Answer 7 · 2026-02-23 10:18:42

52

Views

Quotient map from Sorgenfrey plane to Real Line

Published on 23 Feb 2026 - 10:18

score 109 · Answer 8 · 2026-02-23 10:20:44

109

Views

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

Published on 23 Feb 2026 - 10:20

score 63 · Answer 9 · 2026-02-23 10:16:46

63

Views

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

Published on 23 Feb 2026 - 10:16

score 613 · Answer 10 · 2026-02-23 10:22:52

613

Views

Why is the Sorgenfrey Line not second countable?

Published on 23 Feb 2026 - 10:22

score 126 · Answer 11 · 2026-02-23 10:20:32

126

Views

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

Published on 23 Feb 2026 - 10:20

score 128 · Answer 12 · 2026-02-23 10:19:33

128

Views

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

Published on 23 Feb 2026 - 10:19

score 32 · Answer 13 · 2026-02-23 10:18:25

32

Views

Verifying if it is a legitimate basis for a topology

Published on 23 Feb 2026 - 10:18

score 314 · Answer 14 · 2026-02-23 10:18:41

314

Views

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

Published on 23 Feb 2026 - 10:18

score 94 · Answer 15 · 2026-04-09 11:20:07

94

Views

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

Published on 09 Apr 2026 - 11:20

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.

Trending Questions

Popular # Hahtags

Popular Questions