NOTE ON NONPATH-CONNECTED ORTHOMODULAR LATTICES
Eun-Soon Park · Communications of the Korean Mathematical Society · 1995
Some nonpath-connected orthomodular lattices are given : Every infinite direct product of othomodular lattices containing infinitely many non-Boolean factors is a nonpath-connected orthomodular lattice. The orthomodular lattice of all closed subspaces of an infinite dimensional Hilbert space is a nonpath-connected orthomodular lattice.