Definition 1
A topological space is called semicompact if every semiopen cover has a finite subcover.
Definition 2
Same as locally peripherally compact.
Property
The following properties are all for Definition 1.
- [Dorsett1981] A space is semicompact iff it satisfies the following.
- [Ganster1987] A space X is semicompact iff it satisfies the following.
- X is S-closed.
- For every infinite subset S, .
Reference
- Definition 1
- Dorsett, Ch. Semi-compact R1 and product spaces, Bull. Malaysian Math. Soc., 3(2) (1980), 15-19.
- Ch. Dorsett, Semi compactness, semi separation axioms, and product spaces, Bull. Malaysian Math. Soc. (2) 4 (1981), 21-28.
- M. Ganster, Some remarks on strongly compact spaces and semi compact spaces, Bull. Malaysian Math. Soc. (10) 2 (1987), 67-81.
- Definition 2
- K. Morita, On closed mappings. II, Proc. Japan Acad. Vol.33, No.6 (1957) pp.325-327