Preprint No. A-02-01

Gerhard Preuss

A better framework for first countable spaces

Abstract: In the realm of semiuniform convergence spaces first countability is divisible and leads to a well-behaved topological construct with natural function spaces and one-point extensions such that countable products of quotients are quotients. Every semiuniform convergence space (e.g. symmetric topological space, uniform space, filter space etc.) has an underlying first countable space. Several applications of first countability in a broader context than the usual one of topological spaces are studied.

Keywords: First axiom of countability, second axiom of countability, countably compact, sequentially compact, sequentially complete, continous convergence, sequentially continous, semiuniform convergence spaces, convergence spaces, filter spaces, topological spaces, uniform spaces, bicoreflective subconstruct, cartesian closedness

Mathematics Subject Classification (MSC2000): 54A05, 54C35, 54D55, 54E15, 18A40, 18D15

Language: ENG

Available: Pr-A-02-01.ps

Contact: Gerhard Preuss, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (preuss@math.fu-berlin.de)

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