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Abstract

We introduce a new notion called weakly contra-m-continuous functions as functions from a set satisfying some minimal conditions into a topological space. We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of several modifications of weak contra-continuity due to Baker [9].

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Summary We investigate further properties of semi-I-open sets and semi-I-continuous functions introduced in [4] and give the notions of semi-I-open and semi-I-closed functions.

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Abstract

A new kind of sets called generalized w-closed (briefly gw-closed) sets is introduced and studied in a topological space by using the concept of weak structures introduced by Á. Császár in [6]. The class of all gw-closed sets is strictly larger than the class of all w-closed sets. Furthermore, g-closed sets (in the sense of N. Levine [17]) is a special type of gw-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of w-regular and w-normal spaces have been given.

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Summary New classes of sets called O-closed sets and  Os-closed sets are introduced and studied. Also, we introduce and study O-continuous functions and Os-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces O-T 1/2 and O-T s.

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Abstract

We introduce a new notion called contra-(μ,λ)-continuous functions as functions on generalized topological spaces [8]. We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of several modifications of contra-continuity due to Dontchev [18].

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Acta Mathematica Hungarica
Authors: Maximilian Ganster, Saeid Jafari, and Takashi Noiri
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