We begin 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. We reformulate the axioms. Generalized topology is found to be connected with the concept of a bornological universe. Both GTS and its full subcategory SS of small spaces are topological categories. The second part of this paper will also appear in this journal.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-3-1,
author = {Artur Pi\k ekosz},
title = {On generalized topological spaces I},
journal = {Annales Polonici Mathematici},
volume = {107},
year = {2013},
pages = {217-241},
zbl = {1268.54002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-3-1}
}
Artur Piękosz. On generalized topological spaces I. Annales Polonici Mathematici, Tome 107 (2013) pp. 217-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-3-1/