Question

Prob. 7 (a), Sec. 24, in Munkres' TOPOLOGY, 2nd ed: Any order preserving surjective map between ordered sets is a homeomorphism

score 564 · Answer 1 · 2017-12-01 11:42:21

564

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Prob. 7 (a), Sec. 24, in Munkres' TOPOLOGY, 2nd ed: Any order preserving surjective map between ordered sets is a homeomorphism

Published on 01 Dec 2017 - 11:42

score 225 · Answer 2 · 2017-12-20 19:38:01

225

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Separating Closed Sets in a Well-Ordered Set in the Order Topology

Published on 20 Dec 2017 - 19:38

score 1.3k · Answer 3 · 2011-04-22 07:28:43

1.3k

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order topology and discrete topology

Published on 22 Apr 2011 - 7:28

score 1.2k · Answer 4 · 2012-01-24 21:22:49

1.2k

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Closed Intervals of $\omega_1$ Are Compact

Published on 24 Jan 2012 - 21:22

score 366 · Answer 5 · 2012-03-05 13:19:52

366

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Order topology and axiom of choice

Published on 05 Mar 2012 - 13:19

score 7.7k · Answer 6 · 2012-07-01 20:32:53

Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$

score 4.3k · Answer 7 · 2012-07-18 21:49:48

4.3k

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What does order topology over Ordinal numbers look like, and how does it work?

Published on 18 Jul 2012 - 21:49

score 275 · Answer 8 · 2013-02-07 19:46:59

275

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ordered topology

Published on 07 Feb 2013 - 19:46

score 2.5k · Answer 9 · 2013-03-06 16:09:14

2.5k

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Why are ordered spaces normal? [collecting proofs]

Published on 06 Mar 2013 - 16:09

score 701 · Answer 10 · 2013-03-19 00:15:56

701

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What are topological spaces $\omega_1$ and $\omega_1 + 1$?

Published on 19 Mar 2013 - 0:15

score 44 · Answer 11 · 2020-12-09 14:12:46

44

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Conclusion about corollary V.6.1 in Schaeffer & Wolff (Topological Vector Spaces 2nd edition)

Published on 09 Dec 2020 - 14:12

score 53 · Answer 12 · 2020-12-16 18:30:56

53

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Separation axioms of topology

Published on 16 Dec 2020 - 18:30

score 89 · Answer 13 · 2021-02-01 19:07:50

89

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Supremum in a dictionary ordered set.

Published on 01 Feb 2021 - 19:07

score 126 · Answer 14 · 2026-02-23 10:20:32

126

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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 15 · 2021-03-06 17:37:59

128

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What is the topology defined on $[0, \omega_1)$ it and how do we define its basis?

Published on 06 Mar 2021 - 17:37

List Question

Prob. 7 (a), Sec. 24, in Munkres' TOPOLOGY, 2nd ed: Any order preserving surjective map between ordered sets is a homeomorphism

Separating Closed Sets in a Well-Ordered Set in the Order Topology

order topology and discrete topology

Closed Intervals of $\omega_1$ Are Compact

Order topology and axiom of choice

Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$

What does order topology over Ordinal numbers look like, and how does it work?

ordered topology

Why are ordered spaces normal? [collecting proofs]

What are topological spaces $\omega_1$ and $\omega_1 + 1$?

Conclusion about corollary V.6.1 in Schaeffer & Wolff (Topological Vector Spaces 2nd edition)

Separation axioms of topology

Supremum in a dictionary ordered set.

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

What is the topology defined on $[0, \omega_1)$ it and how do we define its basis?

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