On PC-compact spaces
by
Saeid Jafari
Department of Mathematics and Physics, Roskilde University, Denmark
Coauthors: Maximilian Ganster (Graz University of Technology, Austria), Takashi Noiri (Yatsushiro College of Technology, Japan)

In 1989, Khadra [1] introduced a new type of compactness called p-closedness. Dontchev et al. [2] further investigated p-closed spaces and obtained many properties. It turns out that p-closedness is placed strictly between strong compactness [3] and quasi-H-closedness [4]. On the other hand, Viglino [5] introduced and studied the notion of C-compact spaces. It is the intention of this talk to offer another form of compactness called PC-compactness analogous to C-compact spaces. We also give several of its properties and show that it is weaker than strong compactness and stronger than both p-closedness and C-compactness.

[1] Abd El-Aziz Ahmad Abo-Khadra, On generalized forms of compactness, Master's Thesis, Faculty of Sciences, Tanta University, Egypt 1989.

[2] J. Dontchev, M. Ganster and T. Noiri, On p-closed spaces, Internat. J. Math. Math. Sci. 24(2000), 203-212.

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

[4] J. Porter and J. Thomas, On H-closed and minimal Hausdorff spaces, Trans. Amer. Math. Soc. 138(1969), 159-170.

[5] G. Viglino, C-compact spaces, Duke Math. J. 36(1969), 761-764.

Date received: April 23, 2001