Sequential Topologies on Boolean Algebras

Abstract

A priori limit operator>. maps sequence of a set X into a subset of X. There exists maximal topology on X such that for each sequence x there holds >.(x) C limx. The space obtained in such way is always sequential. If a priori limit operator each sequence x which satisfy lim sup x = lim inf x maps into {lim sup x}, then we obtain the sequential topology Ts. If a priori 'limit operator maps each sequence x into {lim sup x}, we obtain topology denoted by aT. Properties of these topologies, in general, on class of Boolean algebras with condition (Ii) and on class of weakly-distributive b-cc algebras are investigated. Also, the relations between these classes and other classes of Boolean algebras are considered.

A priori limit operator A svakom nizu elemenata skupa X dodeljuje neki podskup skupa X. Tada na skupu X postoji maksimalna topologija takva da za svaki niz x vazi A(X) c lim x. Tako dobijen prostor je uvek sekvencijalan. Ako a priori limit operator svakom nizu x koji zadovoljava uslov lim sup x = liminfx dodeljuje skup {limsupx} onda se, na gore opisan nacin, dobija tzv. sekvencijalna topologija Ts. Ako a priori limit operator svakom nizu x dodeljuje {lim sup x}, dobija se topologija oznacena sa OT. Ispitivane su osobine ovih topologija, generalno, na klasi Bulovih algebri koje zadovoljavaju uslov (Ii) ina klasi slabo-distributivnih i b-cc algebri, kao i odnosi ovih klasa prema drugim klasama Bulovih algebri.