Question

Explicit construction of the join of an arbitrary set in the lattice of partitions?

score 82 · Answer 1 · 2021-12-01 15:35:04

82

Views

Explicit construction of the join of an arbitrary set in the lattice of partitions?

Published on 01 Dec 2021 - 15:35

score 884 · Answer 2 · 2021-12-02 11:19:15

884

Views

Prove that every non-empty finite subset of a lattice has a least upper bound and a greatest lower bound

Published on 02 Dec 2021 - 11:19

score 57 · Answer 3 · 2021-12-10 09:32:41

57

Views

In a finite poset $P$, a down-set $I$ is meet-irreducible $\iff I=P\backslash\uparrow x$ for some $x\in P$

Published on 10 Dec 2021 - 9:32

score 86 · Answer 4 · 2021-12-10 17:43:19

86

Views

Let $A_1$, $A_2$, $P$ be CPOs and let $\psi: A_1 \times A_2 \to P $ be a map, then $\psi$ is continuous $\iff$ it is so in each variable separately

Published on 10 Dec 2021 - 17:43

score 29 · Answer 5 · 2021-12-10 22:24:50

29

Views

Converse to a proposition on lattices and join-irreducible elements

Published on 10 Dec 2021 - 22:24

score 82 · Answer 6 · 2021-12-11 10:45:13

82

Views

$P$ be a poset and $X, Y \subseteq P$. Is it true that if $\downarrow X = \downarrow Y$ , then $X= Y$?

Published on 11 Dec 2021 - 10:45

score 29 · Answer 7 · 2026-03-25 09:29:50

29

Views

$I(A)$ and $I(B)$ ideal lattices, then $F(J) = \downarrow \psi(J)$ and $G(U)=\downarrow \phi(U)$ is a connection of Galois between $I(A)$ and $I(B)$.

Published on 25 Mar 2026 - 9:29

score 46 · Answer 8 · 2021-12-12 09:25:06

46

Views

$P$ poset. $x = \bigvee(\downarrow x\cap U)\Rightarrow \forall x, y \in P$, with $y \lt x$, $\exists a\in U$ s.t. $a \le x $ and $a \nleqslant y$

Published on 12 Dec 2021 - 9:25

score 328 · Answer 9 · 2021-12-12 13:16:26

328

Views

$L$ finite and distributive lattice, then $\mathcal{J}(L)$ (join-irreducible's) is isomorphic, as poset, to $\mathcal{M}(L)$ (meet-irreducible's)

Published on 12 Dec 2021 - 13:16

score 121 · Answer 10 · 2021-12-14 03:22:06

121

Views

Lattice under a product oder

Published on 14 Dec 2021 - 3:22

score 49 · Answer 11 · 2026-03-30 02:07:57

49

Views

Which are the latticial properties of the quartered aztec diamond?

Published on 30 Mar 2026 - 2:07

score 73 · Answer 12 · 2021-12-19 14:47:54

73

Views

Symmetric relations form a CABA

Published on 19 Dec 2021 - 14:47

score 36 · Answer 13 · 2021-12-22 15:55:58

36

Views

Need a clarification of the proof that the prime ideal space of a distributive bounded lattice is compact

Published on 22 Dec 2021 - 15:55

score 105 · Answer 14 · 2026-03-30 02:11:25

105

Views

In a distributive lattice, which are the equivalence classes of the projectivity relation on prime intervals?

Published on 30 Mar 2026 - 2:11

score 73 · Answer 15 · 2021-12-23 14:42:14

73

Views

let $L$ be a bounded distributive lattice with dual space $(X:=\mathcal{I}_p(L), \subseteq, \tau)$, then the clopen downsets of $X$ are $X_a, a \in L$

Published on 23 Dec 2021 - 14:42

List Question

Explicit construction of the join of an arbitrary set in the lattice of partitions?

Prove that every non-empty finite subset of a lattice has a least upper bound and a greatest lower bound

In a finite poset $P$, a down-set $I$ is meet-irreducible $\iff I=P\backslash\uparrow x$ for some $x\in P$

Let $A_1$, $A_2$, $P$ be CPOs and let $\psi: A_1 \times A_2 \to P $ be a map, then $\psi$ is continuous $\iff$ it is so in each variable separately

Converse to a proposition on lattices and join-irreducible elements

$P$ be a poset and $X, Y \subseteq P$. Is it true that if $\downarrow X = \downarrow Y$ , then $X= Y$?

$I(A)$ and $I(B)$ ideal lattices, then $F(J) = \downarrow \psi(J)$ and $G(U)=\downarrow \phi(U)$ is a connection of Galois between $I(A)$ and $I(B)$.

$P$ poset. $x = \bigvee(\downarrow x\cap U)\Rightarrow \forall x, y \in P$, with $y \lt x$, $\exists a\in U$ s.t. $a \le x $ and $a \nleqslant y$

$L$ finite and distributive lattice, then $\mathcal{J}(L)$ (join-irreducible's) is isomorphic, as poset, to $\mathcal{M}(L)$ (meet-irreducible's)

Lattice under a product oder

Which are the latticial properties of the quartered aztec diamond?

Symmetric relations form a CABA

Need a clarification of the proof that the prime ideal space of a distributive bounded lattice is compact

In a distributive lattice, which are the equivalence classes of the projectivity relation on prime intervals?

let $L$ be a bounded distributive lattice with dual space $(X:=\mathcal{I}_p(L), \subseteq, \tau)$, then the clopen downsets of $X$ are $X_a, a \in L$

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