A better framework for first countable spaces

Authors

  • Gerhard Preuss Free University Berlin

DOI:

https://doi.org/10.4995/agt.2003.2034

Keywords:

First axiom of countability, Second axiom of countability, Countably compact, Sequentially compact, Sequentially complete, Continuous convergence, Sequentially continuous, Semiuniform convergence spaces, Convergence spaces, Filter spaces, Topological spac

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.

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Author Biography

Gerhard Preuss, Free University Berlin

Department of Mathematics and Computer Science

References

H.L. Bentley, H. Herrlich and W.A. Robertson, Convenient categories for topologists, Comm. Math. Univ. Carolinae 17 (1976), 207-227.

W. Gähler, Grundstrukturen der Analysis I/II (Birkhäuser, Basel, 1977/78). http://dx.doi.org/10.1007/978-3-0348-5572-3

H. Hahn, Theorie der reellen Funktionen (Berlin, 1921). http://dx.doi.org/10.1007/978-3-642-52624-4

G. PreuB, Semiuniform convergence spaces, Math. Japonica 41 (1995), 465-491.

G. PreuB, Foundations of Topology - An Approach to Convenient Topology (Kluwer, Dordrecht, 2002).

W.A. Robertson, Convergence as a nearness concept, PhD thesis (Carlton University, Ottawa, 1975).

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Published

2003-10-01

How to Cite

[1]
G. Preuss, “A better framework for first countable spaces”, Appl. Gen. Topol., vol. 4, no. 2, pp. 289–299, Oct. 2003.

Issue

Section

Regular Articles