On generalized topological spaces

TL;DR

This paper systematically studies the category of generalized topological spaces, exploring their properties and how they relate to locally definable and weakly definable spaces within weakly topological structures.

Contribution

It provides new completeness and cocompleteness results for the category of generalized topological spaces, expanding the theoretical framework.

Findings

Achieved completeness and cocompleteness results.

Connected generalized topological spaces to locally definable spaces.

Enhanced understanding of weakly topological structures.

Abstract

In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved. Generalized topological spaces help to reconstruct the important elements of the theory of locally definable and weakly definable spaces in the wide context of weakly topological structures.