We introduce the class of S-paracompact spaces as a generalization of paracompact spaces. A space (X,T) is S-paracompact if every open cover of X has a locally finite semi-open refinement. We characterize S-paracompact spaces and study their basic properties. The relationships
between S-paracompact spaces and other well-known spaces are investigated.
We introduce the operator given by a hereditary class and a generalized topology μ, and investigate its properties. With the help of , we define -semi-open sets which are generalized open sets on generalized topologies and study the relation between such sets and some generalized open sets (e.g. μ-semi-open sets, μ-β-open sets) on generalized topologies.
We introduce generalized continuous functions defined by generalized open (= g-α-open, g-semi-open, g-preopen, g-β-open) sets in generalized topological spaces which are generalized (g, g′)-continuous functions. We investigate characterizations and relationships among such functions.
Authors:Franco Barragán, Sergio Macías, and Anahí Rojas
Let X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱn(X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : X → X, we consider the induced functions ℱn(ƒ): ℱn(X) → ℱn(X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒ ∈ M and ℱn(ƒ) ∈ M.