Abstract
We consider the Category of Sheaves of Sets. The morphisms are chosen in such a way that a change of the base space is allowed via continuous functions. Following M. M. Clementina, E. Giuli and W. Tholen in "Topology in a Category: Compactness", we define a proper (E, M)factorization system for morphisms and a closure operator with respect to M. The Stone-Cech compactification is defined for any sheaf (E, p, T) of sets by adapting standard germination processes to construct a sheaf over the Stone-Cech compactification BT (of) T. We prove that the sheaf constructed satisfies a suitable universal property characterizing the Stone-Cech compactification of a sheaf of sets.
Keywords
References
J. Adámek et al, Abstract and Concrete Categories. The Joy of Cats, Wiley & Sons, (1990).
S. Bautista & J. Varela, On the co-completness of the category of Hausdorff uniform spaces, Rev. Colombiana Mat. 21 (1997), 109-114.
M. M. Clementino, E. Giulll & W. Tholen Topology in a Category: Compactness, Portugaliae Mathematica 53 (Fase. 4) (1996).
R. De Castro & J. Varela, Germination in bundles of uniform spaces, Rev. Colombiana Mat. 24 (1990), 103-112.
C. M. Neira, Sobre Campos de Espacios Uniformes, Doctoral Dissertation, Universidad Nacional de Colombia, to appear.
J. Varela, On the existence of uniform bundles, Rev. Colombiana Mat. 24 (1995), 95-101.
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright (c) 2024 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales