Path-connected and non path-connected orthomodular lattices
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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∩B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A∩B|<∞ 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]∨ generated by the commutators of L is finite, then L is path-connected.
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∩B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A∩B|<∞ 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]∨ generated by the commutators of L is finite, then L is path-connected.
참고문헌 (9)
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