Profinite orthomodular lattices Academic Article uri icon

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abstract

  • We prove that any compact topological orthomodular lattice L L is zero dimensional. This leads one to show that L L is profinite iff it is the product of finite orthomodular lattices with their discrete topologies. We construct a completion L ¯ \overline L of a residually finite orthomodular lattice L L having the property that every element of L ¯ \overline L is the join of meets of elements of L L . Necessary and sufficient conditions for L L that L ¯ \overline L is the MacNeille completion are obtained.

publication date

  • January 1, 1993