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Acta Mathematica Hungarica
Authors: Aslı Güldürdek and Oya Bedre Özbakır
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Summary  

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.

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Abstract  

Some properties of two classes of functions (p.a.α.c. and p.s.w.c) are studied.

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Summary In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened.

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Abstract  

The definition of the product of topologies is generalized in such a way that topologies are replaced by generalized topologies in the sense of [3].

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Summary  

Several concepts generalizing the notion of connectedness of a topological space are investigated. It is obtained that some of these concepts are equivalent (without or with additional conditions).

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Abstract

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.

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Abstract  

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.

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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 : XX, 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: ƒM and ℱn(ƒ) ∈ M.

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