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p-compact の変更点


 *Definition [#n9654393]
 p denotes an ultrafilter on ω, the set of natural numbers.
 p denotes a free ultrafilter on ω, the set of natural numbers.
 Let X be a topological space, (S_n) a sequence of nonempty subsets in X. A point x in X is called a p-limit point of (S_n) if for all neighborhood V of x, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5c%7bn%5cin%5comega:V%5ccap%20S_n%5cneq%5cemptyset%5c%7d%5cin%20p$%7d%25.png);.
 If (x_n) is a sequence of points in X, "a p-limit point of (x_n)" means a p-limit point of a sequence of singleton ({x_n}).
 X is said to be p-compact if every sequence (x_n) has a p-limit point.
 
 *Remark [#sdc17453]
 -If X is p-compact for all p, X is called [[ultracompact]].
 -For the term in bitopology, see [[p-compact in bitopology]].
 
 *Reference [#d0ffabb7]
 -A. R. Bernstein, ''A new kind of compactness for topological spaces'', Fund.Math. 66 (1970), 185-193.