Paper read at the Second Symposium on Categorical Topology at the University of Cape Town 9–13 August 1976

T₀-SEPARATION IN TOPOLOGICAL CATEGORIES

Published in: Quaestiones Mathematicae
Volume 2 , issue 1-3 , 1977 , pages: 177–190

DOI: 10.1080/16073606.1977.9632541

Author(s): J.M. Harvey Department of Mathematics, Rhodesia

Keywords: 18A99 , 18D99 , 54D10 , 54E15

Abstract

R.-E. Hoffmann [5,6] has introduced the notion of an (E,M)-universally topological functor, which provides a categorical characterization of the T₀-separation axiom of general topology. In this paper, we characterise these functors in terms of the unique extension of structure functors defined on the subcategory of “separated” objects (of the domain category). This, in turn, leads to a solution of some problems due to G.C.L. Brümmer [1,2]. Other results include a generalization of L. Skula's characterization of the bireflective subcategories of Top [10].

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