On generalized topological spaces I
Volume 107 / 2013
Annales Polonici Mathematici 107 (2013), 217-241
MSC: Primary 54A05; Secondary 18F10, 46A17.
DOI: 10.4064/ap107-3-1
Abstract
We begin a systematic study of the category $\mathbf{GTS}$ of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings. We reformulate the axioms. Generalized topology is found to be connected with the concept of a bornological universe. Both $\mathbf{GTS}$ and its full subcategory $\mathbf{SS}$ of small spaces are topological categories. The second part of this paper will also appear in this journal.
