IJPAM: Volume 43, No. 3 (2008)
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.
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
