Strongly compact spaces characterized via multifunctions
by
Saeid Jafari
Department of Mathematics and Physics, Roskilde University, Postbox 260, 4000 Roskilde, Denmark
Coauthors: Takashi Noiri (Yatsushiro College of Technology)

Atia et al. [1] introduced a strong version of compactness called strong compactness. In 1984, Mashhour et al. [4] introduced the notion of strongly compact relative to a topological space and established several characterizations of these spaces. In 1987, Ganster [2] obtained an interesting result that there exist no infinite spaces which are both strongly compact and semi compact. He also proved that a topological space is strongly compact if and only if it is compact and that every infinite subset of X has nonempty interior. In 1988, Jankovic et al. [3] have shown that a topological space (X, T) is strongly compact if and only if it is compact and the family of dense sets in (X, T) is finite.

It is the object of this talk to give some characterizations of 1-lower and 1-upper precontinuous multifunctions and then by using them we give some characterizations of strongly compact spaces.

References

[1] R. H. Atia, S. N. El-Deeb and I. A. Hasanein, A note on strong compactness and S-closedness, Mat. Vesnik 6(19)(1982), 23-28.

[2] M. Ganster, Some remarks on strongly compact spaces and semi compact spaces, Bull. Malaysia Math. Soc. (10)2(1987), 67-81.

[3] D. S. Jankovic, I. Reilly and M. K. Vamanamurthy, On strongly compact topological spaces, Q & A in General Topology, vol. 6(1988), 29-39.

[4] A. S.Mashhour, M. Abd El-Monsef, I. A. Hasanein and T. Noiri, Strongly compact spaces, Delta J. Sci. 8(1984), 30-46.

Date received: April 13, 2000