Order convergence and convergence almost everywhere revisited

In Analysis two modes of non-topological convergence are interesting: order convergence and convergence almost everywhere. It is proved here that oder 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 obtained in a more indirect way by using fuzzy topologies

Connectedness, disconnectedness, and light factorization structures in a fuzzy setting

Connectedness, disconnectedness, and light factorization structures are studied in the realm of the topological constructs \textbf{FPUConv} and \textbf{FSUConv} of fuzzy preuniform convergence spaces and fuzzy semiuniform convergence spaces respectively which have been introduced by the author in \cite{23} using fuzzy filters in the sense of Eklund and Gähler \cite{7}. The presented theory profits from the fact that both constructs have hereditary quotients. Additionally, there are special features, e.g. a product theorem for the investigated connectedness concept and the existene of a proper class of light factorization structures on FPUConv as well as on FSUConv

Der Nachlass Oskar Tenges in der Landesbibliothek Oldenburg : Katalog

bearb. von Gerhard Preuß. Mit einem Beitrag von Wolfgang Hartung und einem unveröffentlichten Vortrag von Oskar Tenge: SturmflutenDie Vorlage enth. insgesamt 2 Werk

Convenient Topology

. A new viewpoint of Topology, summarized under the name Convenient Topology, is considered in such a way that the structural deficiencies of topological and uniform spaces are remidied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this context semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, namely simple convergence, continuous convergence and uniform convergence. Several results are presented which cannot be obtained by using topological or uniform spaces respectively. Mathematics Subject Classifications (1991). 54A05, 54A20, 5..

Completion Of Semiuniform Convergence Spaces

. Semiuniform convergence spaces form a common generalization of filter spaces (including symmetric convergence spaces [and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform convergence space a completion is constructed, called the simple completion. This one generalizes Cs'asz'ar's --completion of filter spaces. Thus, filter spaces are characterized as subspaces of convergence spaces. Furthermore, Wyler's completion of separated uniform limit spaces can be easily derived from the simple completion. Mathematics Subject Classifications (1991). 54A05, 54A20, 54E15, 54E52, 18A40. Keywords: Semiuniform convergence spaces, filter spaces, uniform convergence spaces (= uniform limit spaces), completions, universal constructions. 1. Introduction In 1967 Cook and Fischer [5..