On dimension and weight of a local contact algebra

TL;DR

This paper introduces notions of weight and dimension for local contact algebras and proves their equivalence to topological properties of locally compact Hausdorff spaces, extending duality results.

Contribution

It defines weight and dimension for local contact algebras and establishes their correspondence with topological invariants of spaces under duality.

Findings

w(X)=w(L(X)) for locally compact Hausdorff spaces

dim(X)=dim(L(X)) for normal locally compact Hausdorff spaces

extends duality to include topological invariants

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)).