Original Articles

T_o-OBJECTS AND SEPARATED OBJECTS IN TOPOLOGICAL CATEGORIES

Published in: Quaestiones Mathematicae
Volume 14 , issue 3 , 1991 , pages: 315–325

DOI: 10.1080/16073606.1991.9631649

Author(s): Sibylle Weck-Schwarz Department of Mathematics, South Africa

Keywords: 54D10 , 54B30 , 18B99 , 54A05 , 54A20 , 54D10 , 54B30 , 18B99 , 54A05 , 54A20

Abstract

Several well-known generalizations of the usual topological T_o-axiom to topological categories are compared. It is shown that they lead to two different concepts: T_o and separatedness. The resulting sub-categories are characterized for some important categories of convergence spaces. They provide natural examples disproving the equivalence of the two concepts. Necessary and sufficient conditions are given for the T_o-objects and separated objects to coincide.

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