Question

Solution verification: Show that $a_1 <_{(-1,1)} a_2\implies f(a_1)<_{\mathbb{R}} < f(a_2)$ to prove $(-1,1)$ has the same order type as $\mathbb{R}$

score 56 · Answer 1 · 2026-04-14 20:06:28

56

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Solution verification: Show that $a_1 <_{(-1,1)} a_2\implies f(a_1)<_{\mathbb{R}} < f(a_2)$ to prove $(-1,1)$ has the same order type as $\mathbb{R}$

Published on 14 Apr 2026 - 20:06

score 134 · Answer 2 · 2026-04-11 18:47:32

134

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A clarification regarding maximal linearly ordered subsets and the Hausdorff maximal principle

Published on 11 Apr 2026 - 18:47

score 101 · Answer 3 · 2026-04-12 13:38:06

101

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Show the existence of positive linear functional whose values lies in given interval

Published on 12 Apr 2026 - 13:38

score 53 · Answer 4 · 2026-04-16 03:59:17

53

Views

Reference for Jech's notion of stationary set

Published on 16 Apr 2026 - 3:59

score 78 · Answer 5 · 2026-04-11 13:27:08

78

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Is the identity function the only order-preserving isomorphism between a linearly-ordered set and itself?

Published on 11 Apr 2026 - 13:27

score 39 · Answer 6 · 2026-04-16 01:40:42

39

Views

Countryman type is a Specker type: an unclear point in the proof

Published on 16 Apr 2026 - 1:40

score 28 · Answer 7 · 2026-04-09 10:47:14

28

Views

Pronouncing Statements About Partial Orders

Published on 09 Apr 2026 - 10:47

score 40 · Answer 8 · 2026-04-15 09:02:45

40

Views

A formalization of the notion of Hasse diagrams

Published on 15 Apr 2026 - 9:02

score 60 · Answer 9 · 2026-04-15 23:04:11

60

Views

Maximal element by vacuous truth

Published on 15 Apr 2026 - 23:04

score 49 · Answer 10 · 2026-04-16 06:36:45

49

Views

Discussing Ex 13. Section 3. p-29, Munkres' Topology 2E.

Published on 16 Apr 2026 - 6:36

score 234 · Answer 11 · 2026-04-14 02:33:50

234

Views

Finding all bijections $f : \mathbb{N}^+ \to \mathbb{N}^+$ satisfying $a \mid b \Rightarrow f(a) \mid f(b)$

Published on 14 Apr 2026 - 2:33

score 37 · Answer 12 · 2026-04-14 12:25:09

37

Views

Lattice automorphisms of a countable product of copies of ${\mathbb N}$

Published on 14 Apr 2026 - 12:25

score 80 · Answer 13 · 2026-04-15 06:15:05

80

Views

Partially ordered sets and ordinals

Published on 15 Apr 2026 - 6:15

score 90 · Answer 14 · 2026-04-16 01:49:14

90

Views

Discussion of Exercise 9, section 4 on page 35 of Munkres’ Topology 2E.

Published on 16 Apr 2026 - 1:49

score 52 · Answer 15 · 2026-04-16 02:08:45

52

Views

Do $\{0, 1\}×N$ and $N×\{0, 1\}$ have the same order type?

Published on 16 Apr 2026 - 2:08

List Question

Solution verification: Show that $a_1 <_{(-1,1)} a_2\implies f(a_1)<_{\mathbb{R}} < f(a_2)$ to prove $(-1,1)$ has the same order type as $\mathbb{R}$

A clarification regarding maximal linearly ordered subsets and the Hausdorff maximal principle

Show the existence of positive linear functional whose values lies in given interval

Reference for Jech's notion of stationary set

Is the identity function the only order-preserving isomorphism between a linearly-ordered set and itself?

Countryman type is a Specker type: an unclear point in the proof

Pronouncing Statements About Partial Orders

A formalization of the notion of Hasse diagrams

Maximal element by vacuous truth

Discussing Ex 13. Section 3. p-29, Munkres' Topology 2E.

Finding all bijections $f : \mathbb{N}^+ \to \mathbb{N}^+$ satisfying $a \mid b \Rightarrow f(a) \mid f(b)$

Lattice automorphisms of a countable product of copies of ${\mathbb N}$

Partially ordered sets and ordinals

Discussion of Exercise 9, section 4 on page 35 of Munkres’ Topology 2E.

Do $\{0, 1\}×N$ and $N×\{0, 1\}$ have the same order type?

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