Question

Bijection between ideals of a poset and order-preserving maps from the poset to $\{0,1\}$.

score 238 · Answer 1 · 2018-09-22 00:31:02

238

Views

Bijection between ideals of a poset and order-preserving maps from the poset to $\{0,1\}$.

Published on 22 Sep 2018 - 0:31

score 110 · Answer 2 · 2026-03-25 18:49:48

110

Views

Why do the $-1$-categories form a categeory rather than merely a set?

Published on 25 Mar 2026 - 18:49

score 188 · Answer 3 · 2018-09-24 16:18:39

Suppose that every nonempty subset $X$ bounded from above has a supremum. Then every nonempty subset $Y$ bounded from below has an infimum

score 190 · Answer 4 · 2018-09-26 16:46:31

190

Views

Is continuity of a total preorder is preserved under a continuous order-preserving map?

Published on 26 Sep 2018 - 16:46

score 52 · Answer 5 · 2026-03-25 03:04:12

52

Views

There is equivalence of norms and equivalence of metrics. Is there equivalence of order relations?

Published on 25 Mar 2026 - 3:04

score 83 · Answer 6 · 2018-09-27 02:07:54

83

Views

If $(A_1,<_1)$ and $(A_2,<_2)$ are linearly ordered sets and $|A_1|=|A_2|<\aleph_0$. Then $(A_1,<_1)$ and $(A_2,<_2)$ are isomorphic

Published on 27 Sep 2018 - 2:07

score 217 · Answer 7 · 2018-09-27 12:19:59

217

Views

Every countable linearly ordered set is similar to one of its subsets

Published on 27 Sep 2018 - 12:19

score 759 · Answer 8 · 2018-09-27 15:05:33

A proper subset of $\Bbb Q$ that is order-isomorphic to $\Bbb Q$; An infinite set that is NOT order-isomorphic to any of its proper subset

score 147 · Answer 9 · 2018-09-28 02:22:47

Let $(P,<)$ and $(Q,\prec)$ be countable, dense, and linearly ordered sets without endpoints. Then $(P,<)$ and $(Q,\prec)$ are order-isomorphic

score 106 · Answer 10 · 2018-09-28 08:58:20

106

Views

Confusion about the uniqueness (up to isomorphism) of $(\Bbb R,<)$

Published on 28 Sep 2018 - 8:58

score 88 · Answer 11 · 2018-09-28 09:30:09

88

Views

Example of a preorder on the set of real numbers

Published on 28 Sep 2018 - 9:30

score 3.1k · Answer 12 · 2018-09-29 03:03:15

3.1k

Views

Number of distinct total orders on a set

Published on 29 Sep 2018 - 3:03

score 387 · Answer 13 · 2018-09-29 10:15:10

387

Views

The uniqueness (up to isomorphism) of the complete linear ordering that has a countable dense subset

Published on 29 Sep 2018 - 10:15

score 70 · Answer 14 · 2018-09-29 14:53:04

Let $(P,<)$ and $(Q,\prec)$ be order isomorphic. What kind of properties that $P$ and $Q$ have in common by the order isomorphism?

score 124 · Answer 15 · 2026-03-25 12:37:39

124

Views

Show poset in sage enlarging it

Published on 25 Mar 2026 - 12:37

List Question

Bijection between ideals of a poset and order-preserving maps from the poset to $\{0,1\}$.

Why do the $-1$-categories form a categeory rather than merely a set?

Suppose that every nonempty subset $X$ bounded from above has a supremum. Then every nonempty subset $Y$ bounded from below has an infimum

Is continuity of a total preorder is preserved under a continuous order-preserving map?

There is equivalence of norms and equivalence of metrics. Is there equivalence of order relations?

If $(A_1,<_1)$ and $(A_2,<_2)$ are linearly ordered sets and $|A_1|=|A_2|<\aleph_0$. Then $(A_1,<_1)$ and $(A_2,<_2)$ are isomorphic

Every countable linearly ordered set is similar to one of its subsets

A proper subset of $\Bbb Q$ that is order-isomorphic to $\Bbb Q$; An infinite set that is NOT order-isomorphic to any of its proper subset

Let $(P,<)$ and $(Q,\prec)$ be countable, dense, and linearly ordered sets without endpoints. Then $(P,<)$ and $(Q,\prec)$ are order-isomorphic

Confusion about the uniqueness (up to isomorphism) of $(\Bbb R,<)$

Example of a preorder on the set of real numbers

Number of distinct total orders on a set

The uniqueness (up to isomorphism) of the complete linear ordering that has a countable dense subset

Let $(P,<)$ and $(Q,\prec)$ be order isomorphic. What kind of properties that $P$ and $Q$ have in common by the order isomorphism?

Show poset in sage enlarging it

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