  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.
