IJPAM: Volume 43, No. 3 (2008)


Dieter Leseberg
Department of Mathematics and Informatics
Free University of Berlin
45, Habelschwerdter Allee, 14195, Berlin, GERMANY
e-mail: d.lesebergtu-bs.de

Abstract.An account of some important convergence structures is presented. Among them we discuss set-convergence spaces in the sense of Wyler and preuniform convergence spaces in the sense of Preuß. Both form topological universes, and they seem to be good candidates for an intrinsic study within the realm of convenient topology. By bringing them together we consider as a basic concept uniform filters converging to bounded subsets. Thus, in special cases, we recover the constructs of set-convergence spaces and preuniform convergence spaces and moreover obtain an interesting generalization of Cauchy-spaces, here considered as b-filter spaces. This now enables us to simultaneously express generalized ``topological" and ``uniform" aspects by common means.

This paper is dedicated to my TOP-father Gerhard Preuß
on the occasion of his sixtyfifth birthday

Received: December 18, 2007

AMS Subject Classification: 54A20, 54B30, 54E05, 54E15, 54E17

Key Words and Phrases: neighborhood-systems, supertopological spaces, set-convergence spaces, nearness spaces, supernear spaces, filtermerotopic spaces, preuniform convergence spaces, e-convergence, b-filter spaces, b-convergence spaces, strong topological universes, convenient topology

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 3