On dimension and weight of a local contact algebra
Abstract
As proved in [G. Dimov, Acta Mathematica 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)).
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)).
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