Connectedness and local connectedness in Lowen spaces

摘要

A fuzzy connectedness axiom and a matching fuzzy local connectedness are defined in this paper for Lowen spaces. It is shown that such Lowen spaces have properties corresponding to those of traditional connected and locally connected topological spaces. It is also proved that an L-topological space (X, δ) is fuzzy connected (resp., fuzzy locally connected) in our sense if and only if its induced I (L)-topological space (X, ω(δ)) is too. Some related categorical results are also obtained, and a fuzzy version of topological intersection theorems is given by using our notion of connectedness.