This paper is based on the author’s previous work [S4]. We consider fiber-preserving complex dynamics on fiber bundles whose fibers are Riemann spheres and whose base spaces are compact metric spaces. In this context, without any assumption on (semi-)hyperbolicity, we show that the fiberwise Julia sets are uniformly perfect. From this result, we show that, for any semigroup G generated by a com...

In [1] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals (e.g., real semialgebraic or subanalytic sets), and having connected intersections with all translated coordinate cones in Rn. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equ...

We study interior operators and interior structures in a fuzzy setting.We investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

Let mIO(X) be the family of ⋆-open (resp. α-I-open, pre-I-open, semi-I-open, β-I-open, etc.) sets in an ideal topological space (X, τ, I). By using mIO(X), we introduce and investigate notions m-I-continuous multifunction F : I) → (Y, σ) mi⋆ -continuous σ, J). The notion -continuity is a generalization m-I-continuity i⋆-continuity [9].