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The concept of (ϑ,s)-continuity [6] is considered and studied in fuzzy setting. It is seen that althought it is independent with each of the concepts of fuzzy continuity [2], fuzzy σ-continuity [10], fuzzy almost continuity [1] and fuzzy semicontinuity [1]; it implies fuzzy weak continuity [1], but the converse may not be true. The image of a compact fts [2] under a fuzzy (ϑ,s)-continuous surjective function isS-closed [5]. Finally the concepts of fuzzy (ϑ,s)-closed graphs, fuzzy (ϑ,s)-T 2 spaces and fuzzy Urysohn spaces are introduced and mainly their connections with fuzzy (ϑ,s)-continuity are studied.

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Periodica Mathematica Hungarica
Authors: M. E. Abd El-Monsef, S. N. El-Deeb, F. M. Zeyada, and I. M. Hanafy
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Long and Herrington [3] have investigated some properties of the strongly ?-continuous functions. In this paper we strengthen some of these properties of Long and Herrington [3] by studying a new class of functions, called HC-continuous functions.

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