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On the closure of a topology and low separation axioms
by
Maria Luisa Colasante
Universidad de Los Andes, Mérida, Venezuela
Coauthors: C. Uzcátegui and J. Vielma
Let P(X) denote the power set of X. By identifying a set with its characteristic function, we give P(X) the product topology. The closure cl(T) of any topology T on X is the samallest Alexandroff topology containing T ([2]). We present results concerning some low separation axioms that any topology on X shares with T when bounded by T and cl(T). Special consideration is given to the countable case.
References
[1] Lo, J.T.H, Borel sets and separtion axioms, Mathematical Proceedings of the Royal Irish Academy, 101A(2)(2001), 111-123.
[2] C. Uzcátegui and J. Vielam, Alexandroff topologies view as closed sets in the Cantor Cube, Div. Mat. Vol. 13, No.1(2005), 45-53.
Date received: June 2, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxi-23.