IJPAM: Volume 66, No. 1 (2011)

ORDER CONVERGENCE AND
CONVERGENCE ALMOST EVERYWHERE REVISITED

Gerhard Preuß
Department of Mathematics and Informatics
Institute of Mathematics
Free University of Berlin
45, Habelschwerter Allee, Berlin, 14195, GERMANY
e-mail: [email protected]


Abstract.In analysis two modes of non-topological convergence are interesting: order convergence and convergence almost everywhere. It is proved here that order convergence of sequences can be induced by a limit structure, even a finest one, whenever it is considered in $\sigma$-distributive lattices. Since convergence almost everywhere can be regarded as order convergence in a certain $\sigma$-distributive lattice, this result can be applied to convergence of sequences almost everywhere and thus generalizing a former result of U. Höhle [11] obtained in a more indirect way by using fuzzy topologies.

Received: October 21, 2010

AMS Subject Classification: 06B23, 06D75, 28A20, 54A20

Key Words and Phrases: complete lattices, $\sigma$-distributive lattices, convergence almost everywhere, order convergence, limit spaces (=convergence spaces) and generalizations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 1