PATH-CONNECTED AND NON PATH-CONNECTED ORTHOMODULAR LATTICES

Title & Authors
PATH-CONNECTED AND NON PATH-CONNECTED ORTHOMODULAR LATTICES
Park, Eun-Soon; Song, Won-Hee;

Abstract
A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\small{\cap}$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\small{\cap}$ B| < $\small{\infty}$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\small{\vee}$ generated by the commutators of L is finite, then L is pathconnected.
Keywords
orthomodular lattice;with finite sites;path-connected;non pathconnected;Boolean algebra;
Language
English
Cited by
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