Abstract
Abstract
The aim of this work is to develop the theoretical foundations of the theory
of generalized topological spaces, where the main idea is to perform modulo
small sets. The concept of generalized topological space is supported by
the corresponding constructions from lattice theory. The main topological
notions (interior and closure operators, continuous mapping, weight, density,
Lindel of number, product space, etc.) are studied in the framework of generalized
topological space. We develop the notion of generalized spatial locale,
as an alternative motivation for the concept of generalized topological space,
which makes possible to consider the isomorphism between T0 generalized
topological spaces and generalized spatial locales and, moreover, to extend
the classical duality for all T0 topological spaces without any limitation to
sober spaces.
