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 FPUConv as well as on FSUConv.