SOOCHOW JOURNAL OF MATHEMATICS

Volume 27, No. 3, pp. 343-352, July 2001




SOME CLASSES OF COMPACTNESS IN TERMS OF IDEALS


BY


ARAFA A. NASEF



Abstract. The aim of this paper is to introduce and study some types of compactness modulo an ideal called $ \gamma I$-compact space, $ \gamma I$-compact subsets and contably $ \gamma I$-compact spaces via the notion of $ \gamma$-open sets due to Andrijevié [3] and El-Atik [4]. These concepts generalize $ \gamma$-compactness and $ \gamma$-Lindelöfness. Similarities and dissimilarities between them with other known types of compactness are discussed. Also, several of thier topological properties are investigated. Finally, some effects of various kinds of functions on them ae studied.

-------------------------

Received July 31, 2000.

AMS Subject Classification. 54D30, 54C10.

Key words. ideal, I-compact, countably $ I$-compact, $ \gamma$-compact, $ \gamma$-Lindelöf, $ \gamma I$-compact, conutably $ \gamma I$-compact.