Last-modified: 2010-09-03 (金) 00:41:04
A space X is called ultracompact if it is p-compact for every free ultrafilter on ω (the set of natural numbers).
A topological space X is ultracompact iff every subset family N with the properties:
- for any subset A in X, we can pick some R in N such that A or the complement of A is contained in R
- the interiors of members of N cover X has a finite subfamily which covers X.
- Definition 1
- A. R. Bernstein, A new kind of compactness for topological spaces, Fund.Math. 66 (1970), 185-193.
- Definition 2
- D.V.Thampuran, Nets and Compactness, Portugaliae Mathematica Vol.28(1) pp.37-54.