# Tagged Questions

The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.

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### Homotopy type of some lattices with top and bottom removed

The only reaction to this question on math.SE was 21 views in 4 days, so I decided to repost it here. I am not changing anything. There was an interesting question on MO which OP removed by some ...
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### What are the rank 3 boolean intervals [H,G], with G simple group?

The rank $n$ boolean lattice $B_{n}$ is the subset lattice of $\{1,2, \dots , n\}$. The lattice $B_{3}$ is the following: Question: What are the rank $3$ boolean intervals of the form $[H,G]$, ...
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### Does the collection of coverings on a set $X$ form a lattice when ordered by refinement?

This is a follow-up question to this question, prompted by a comment in Todd Trimble's answer. Let $X\neq \emptyset$ be a set. We say that $U\subseteq {\cal P}(X)\setminus \{\emptyset\}$ is a proper ...
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Let $X\neq \emptyset$ be a set. We say that $U\subseteq {\cal P}(X)\setminus \{\emptyset\}$ is a proper covering if $\bigcup U = X$, and for $a\neq b\in U$ we have $a\not\subseteq b$. Let $\text{... 0answers 69 views ### Weak Topology and Domain Theory: Which topology on the function domain restricts to the weak topology on C([0,1])? Let$\mathbb{IR}$be the interval domain over the set$\mathbb{R}$of real numbers, defined by: $$\mathbb{IR} := \{ [a,b] \mid a, b \in \mathbb{R}, a \leq b\} \cup \{ \mathbb{R}\},$$ and ordered by ... 1answer 127 views ### Dye's Theorem for real von Neumann algebras Dye's classical theorem from 1955 states that if$\theta$is a projection orthoisomorphism (i.e., a bijection between the projective lattices that preserves orthogonality - it then automatically ... 0answers 55 views ### Image of composition of integral upper triangular matrices For$A,B$integral upper triangular matrices on$\mathbb{Z}^k$, do we know something about the image$\text{im}(AB)$in terms of$\text{im}(A)$,$\text{im}(B)$, unions, intersections, determinants, ... 0answers 59 views ### Is there an interval of finite groups, at index n, with strictly more elements than the subgroup lattice of any group, of order n? Let$G$be a finite group and$\mathcal{L}(G)$its subgroup lattice. Let$s(n):= max\{|\mathcal{L}(G)| \text{ for } |G|=n \}$. There is an OEIS page for the sequence$s(n)$: A018216 1, 2, 2, 5, 2, ... 2answers 230 views ### A good upper-bound for the cardinal of an interval of finite groups This post is a relative version of General bound for the number of subgroups of a finite group Let$[H,G]$be a interval of finite groups with$|G:H| = n$. Question: What is a good upper-bound of$|[...
Given a complete bounded lattice $L$, what do we know about the possibility of defining an addition operation $+$ that, broadly speaking, behaves like arithmetical addition? By this, I mean that as ...