Between Preopen and Open Sets in Topological Spaces

Halgwrd M. Darwesh

Abstract


The aim of the present paper is to introduce the class of $\omega_{p}$-open sets which is strictly placed between the class of all preopen and the class of all open subsets of $X$. Relationships with some other type of sets are given. Furthermore, we introduce a new type of continuity termed the class of $\omega$-almost continuous functions which is lies strictly between the class of all continuous and the class of all almost-continuous functions. New decompositions of continuity are obtained.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|