Orthocomplemented Lattices Satisfying the Exchange Axiom
Usa Sasaki · Hiroshima Mathematical Journal · 1954
The set of all closed linear manifolds of a ( not necessarily separable) Hilbet space is a (I) complete, (II) relatively atomic, and (IV) orlhocomPlemented lattice satisfying (III) the exchange axiom of MacLane [lJn, together with the following condition: (V) If b, c are orthogonal elements, then it holds (b, c)M, i.e., a~ c implies (a,._, b) ,,...._ c=a ,._, (b ,,...._ c).The purpose of this paper is to study an abstract lattice L satisfying these five conditions (I)-(V).The main results are as follows2> :