All Questions
Tagged with lattice-orders terminology
49
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Boolean algebra is to classical logic like what is to relevant logic?
The Question:
Boolean algebra is to classical logic like what is to relevant logic?
Context:
I guess this is a terminology question, so there's not much I can add, except that I've been interested ...
- 45.7k
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30
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Terminology for non-empty suprema preserving function
Is there an established name for a map of complete lattices $f : L \to L'$ that preserves nonempty suprema? I.e. for all $U \subseteq L$ with $U \neq \emptyset$,
$$ f( \bigvee U) = \bigvee_{u \in U} f(...
- 469
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What is a cone of a lattice?
I'm reading Fulton Harris group representation theory.
I encountered this:
"The virtual characters of $G$ form a lattice $\Lambda \cong \mathbb Z^{\mathfrak c} \in \mathbb C_{\text{class}}(G)$, ...
- 449
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Name of the monotone-like property "$f(x)\geq f(x\wedge y)$ implies $f(x\vee y)\geq f(x)$" on a lattice
Let $(X,\leq)$ be a lattice. There is a function $f$ that has the following property.
$f(x)\geq f(x\wedge y)$ implies $f(x\vee y)\geq f(x)$
where strict inequality on the left-hand side implies ...
- 69
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65
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Semilattice whose Subsets are All Closed -- does it have a special name?
Context: self-education.
I am currently getting my head round semilattices.
My understanding is that a semilattice $(S, \odot)$ is a semigroup whose operation $\odot$ is both commutative and ...
- 5,057
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36
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How is the dual notion of an extensive map called?
While reading about closure operators I encountered the following notion:
Definition. Let $A$ be a partially ordered set. A map $f$ from $A$ to $A$ is extensive if $a ≤ f(a)$ for every element $a$ of ...
- 16.6k
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Is there a name for graphs that appear as Hasse diagrams of finite lattices?
Hasse diagrams
are mathematical diagrams used to represent finite partially ordered sets,
and may be seen as a kind of graph.
Apparently, there are some relations between particular kinds of lattices ...
- 1,148
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1
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203
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How to name a poset in which all nonempty subsets have a supremum?
Let $(X,\leq)$ be a partially ordered set such that each nonempty subset of $X$ has a supremum in $X$.
I have two related questions regarding such structures as $(X,\leq)$:
Question 1:
Is $(X,\leq)$ ...
- 1,148
1
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1
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114
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What is the name for a distributive lattice with only two elements, top and bottom?
Is there a name for a distributive lattice with only two (nonequal) elements, 1 and 0, corresponding to top and bottom, respectively? I was thinking of calling it a trivial lattice, but a trivial ...
- 369
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When are the complemented elements of a bounded lattice neutral?
Given any bounded lattice $\mathcal{L}=(X,\lor,\land,0,1)$ we say any $a\in X$ is complemented if there exists an element $b\in X$ such that $a\lor b=1$ and $a\land b=0$ likewise we refer to any ...
- 10.6k
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67
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Looking for the name of the property used to solve this question: In a lattice if $a≤b≤c$, show that (i)$a⊕b=b*c$ (ii)$(a*b)⊕(b*c)=(a⊕b)*(a⊕c)=b$
I've been trying to solve this question
In a lattice if $a≤b≤c$, show that (i)$a⊕b=b*c$ (ii)$(a*b)⊕(b*c)=(a⊕b)*(a⊕c)=b$
for a while now but I simply can't find anything even remotely related to this ...
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74
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Are these families the clopen sets of some class of topologies?
What would one call a family $\mathcal{F}$ of subsets $X$ such that:
$$(1):X\in\mathcal{F}$$
$$(2):A,B\in\mathcal{F}\implies A\setminus B\in\mathcal{F}$$
$$(3):P\subseteq\mathcal{F}\text{ is a ...
- 10.6k
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Why is a Lattice called so?
Why is a Lattice called so? In my mind, I relate a Lattice to the picture of Lattice seen usually in chemistry.. like that of a salt, in 3-d space.. or just balls stacked in a plane on top of each ...
- 406
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Induced total order on equivalence classes from partial order
Given a poset $\langle S, \leq \rangle$, we can define an equivalence relation on elements such that $a \sim b$ if $a \nleq b$ and $b \nleq a$, and extend via transitivity and reflexivity.
Put ...
- 8,000
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What do you call a "multi-dimensional semilattice?"
Semilattices are useful for modeling certain types of systems that describe precedence or superceding. For example, in a semilattice that models "authority" systems, we can say that the join ...
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