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Results tagged with lattice-theory
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user 38085
The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
2
votes
1
answer
168
views
A non-orthomodular orthocomplemented lattice identity?
Assume you have an orthocomplemented (but possibly not orthomodular) lattice $L$. For $q,r\in L$ say "$q$ and $r$ are in position $p'$" to mean that $q\wedge r^\perp=0$ and $r\wedge q^\perp=0$. Is i …
- 1,307
2
votes
1
answer
329
views
Relative Compactness vs Way Below in Locally Compact Hausdorff Spaces
Let $Y$ be a subset of a locally compact Hausdorff topological space $X$ and consider the following properties.
$\overline{Y}$ is compact.
Every open cover of $X$ has a finite subcover of $Y$.
Cer …
- 1,307
7
votes
Representation theorem for modular lattices?
By adding a couple of conditions we can indeed obtain a representation theorem as the OP suggests. Specifically, von Neumann's coordinatization theorem says that every complemented modular lattice of …
- 1,307
6
votes
1
answer
673
views
Generalizations of Birkhoff's HSP Theorem
Let $\mathbf{C}$ be the class of algebraic structures of some fixed type satisfying some sentence $\phi$. Birkhoff's HSP theorem says that $\mathbf{C}$ is closed under homomorphisms, subalgebras and …
- 1,307