Preprint No. A-09-01

Gerhard Preuß

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

Abstract: 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

Keywords: Connectedness, uniform connectedness, $\PP$-connectedness, light factorization structures for sources, fuzzy topological spaces, fuzzy (quasi) uniform spaces, fuzzy preuniform convergence spaces, fuzzy semiuniform convergence spaces, bireflections, $\mathcal{E}$-reflective hulls.

Mathematics Subject Classification (MSC2000): 54A40, 54D05, 18A32, 18A40

Language: ENG

Available: Pr-A-09-01.ps, Pr-A-09-01.pdf

Contact: Gerhard Preuss, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (preuss@math.fu-berlin.de)

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