Volume 33, No. 4, pp. 579-592, October 2007
Abstract. In this paper, the notions of SN-compactness and countable SN-compactness are introduced in -topological spaces by means of semiclosed -sets. (Countable) SN-compactness implies (countable) N-compactness, but all the converse fail to be true. The following results are showed: (a) Every -set with finite support is SN-compact. (b) The intersection of an (a countable) SN-compact -set and a semiclosed -set is (countable) SN-compact. (c) The irresolute image of an (a countable) SN-compact -set is (countable) SN-compact. (d) SN-compactness can be characterized by means of -nets and -filters.
Received September 27, 2005; revised January 7, 2007; March 24, 2007.
AMS Subject Classification. 54A40, 54D35.
Key words. -topology, semiopen (semiclosed) -set, N-compactness; SN-compactness; countable SN-compactness.
The project is supported by Scientific Research Common
Program of Beijing Municipal Commission of Education
(KM200510009009) and The Basic Research Foundation of Beijing
Institute of Technology, P.R. China.