On dimension and weight of a local contact algebra

Abstract

As proved by Dimov [Acta Math. Hungarica, 129 (2010), 314--349], there exists a duality L between the category HLC of locally compact Hausdorff spaces and continuous maps, and the category DHLC of complete local contact algebras and appropriate morphisms between them. In this paper, we introduce the notions of weight and of dimension of a local contact algebra, and we prove that if X is a locally compact Hausdorff space then w(X)=w(L(X)), and if, in addition, X is normal, then dim(X)=dim(L(X)).