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Last-modified: 2010-08-24 (火) 17:57:44

Definition Edit

Every β-open cover has a finite subcover.

Definition 2 Edit

Let X be a topological space and let U be an open cover. Then X is β-compact iff every subset family N of X with the properties:

  1. for A in U, we can pick R in N such that A or the complement of A is contained in R
  2. the U-interiors of members of N cover X
    has a finite subfamily which covers X.

Property Edit

For definition 1,

Reference Edit

Definition 1
M.E.Abd El-Monsef, R.A.Mahmoud, A.A.Nasef and A.M.Kozae, Some generalized forms of compactness and closedness, Delta J. Sci. 9(2) (1985), 257-269.
Definition 2
D.V.Thampuran, Nets and Compactness, Portugaliae Mathematica Vol.28(1) pp.37-54.
  • M. Ganster, Some remarks on strongly compact spaces and semi compact spaces, Bull. Malaysian Math. Soc. (10) 2 (1987), 67?81.