Question

Prob. 12, Sec. 3 in Munkres' TOPOLOGY, 2nd ed: How to relate these order relations?

score 53 · Answer 1 · 2026-02-26 07:11:40

53

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Prob. 12, Sec. 3 in Munkres' TOPOLOGY, 2nd ed: How to relate these order relations?

Published on 26 Feb 2026 - 7:11

score 79 · Answer 2 · 2026-03-09 06:00:13

79

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Why is the set R = $\{(x,y) \in \mathbb{R} \times \mathbb{R} | |x| < |y| \bigvee x=y) \}$ a partial order?

Published on 09 Mar 2026 - 6:00

score 178 · Answer 3 · 2026-04-06 02:58:28

178

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Motivation for looking at the coalgebra structure of incidence algebra resp. group algebra

Published on 06 Apr 2026 - 2:58

score 56 · Answer 4 · 2015-10-17 20:56:36

56

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Can a Proper Partial Order have a Totally-Ordered 'Spine'?

Published on 17 Oct 2015 - 20:56

score 147 · Answer 5 · 2015-10-18 23:00:31

147

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X is totally ordered under ≤ if and only if X follows the law of trichotomy?

Published on 18 Oct 2015 - 23:00

score 227 · Answer 6 · 2015-10-19 13:09:41

227

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Can we express every partial order with these two combinators?

Published on 19 Oct 2015 - 13:09

score 4.1k · Answer 7 · 2015-10-19 21:20:27

4.1k

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How to find a linear extension of a poset

Published on 19 Oct 2015 - 21:20

score 303 · Answer 8 · 2015-10-20 06:59:15

303

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Lexicographic order is a partial order on the the set of all partitions of the positive integer n.

Published on 20 Oct 2015 - 6:59

score 318 · Answer 9 · 2015-10-21 11:42:08

318

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A set with a maximal element but not supremum?

Published on 21 Oct 2015 - 11:42

score 118 · Answer 10 · 2015-10-23 00:42:55

118

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A formula for a monotone bijection between two intervals in $\mathbb Q$

Published on 23 Oct 2015 - 0:42

score 565 · Answer 11 · 2015-10-23 20:28:20

565

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Monotonic function which is not an order-embedding

Published on 23 Oct 2015 - 20:28

score 58 · Answer 12 · 2026-03-29 04:32:55

58

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Function on power set: Negativity implication leads to monotonicity

Published on 29 Mar 2026 - 4:32

score 148 · Answer 13 · 2015-10-27 13:15:42

148

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Show that $\mathbb N $ with the usual order is well ordered.

Published on 27 Oct 2015 - 13:15

score 103 · Answer 14 · 2015-10-28 15:33:34

103

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Partial Orders: "Minimum property" iff "Maximum property"?

Published on 28 Oct 2015 - 15:33

score 46 · Answer 15 · 2015-10-28 18:29:11

46

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$M=\lbrace \frac{(-1)^n}{n}:n \in \mathbb N \rbrace$ not orderly countable

Published on 28 Oct 2015 - 18:29

List Question

Prob. 12, Sec. 3 in Munkres' TOPOLOGY, 2nd ed: How to relate these order relations?

Why is the set R = $\{(x,y) \in \mathbb{R} \times \mathbb{R} | |x| < |y| \bigvee x=y) \}$ a partial order?

Motivation for looking at the coalgebra structure of incidence algebra resp. group algebra

Can a Proper Partial Order have a Totally-Ordered 'Spine'?

X is totally ordered under ≤ if and only if X follows the law of trichotomy?

Can we express every partial order with these two combinators?

How to find a linear extension of a poset

Lexicographic order is a partial order on the the set of all partitions of the positive integer n.

A set with a maximal element but not supremum?

A formula for a monotone bijection between two intervals in $\mathbb Q$

Monotonic function which is not an order-embedding

Function on power set: Negativity implication leads to monotonicity

Show that $\mathbb N $ with the usual order is well ordered.

Partial Orders: "Minimum property" iff "Maximum property"?

$M=\lbrace \frac{(-1)^n}{n}:n \in \mathbb N \rbrace$ not orderly countable

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