On cardinalities of open m-in-n families
by
S. A. Peregudov
State University of Management,Moscow,Russia

If m and n are cardinals, then a family of sets is said to be m-in-n if every set of cardinality m is contained no more than members of the family. m-in- < n is similarly defined. Topological spaces with m-in-n bases have been studies since 1976 (R.W. Heath and W.E. Lindgren considered cases of 2-in- < \omega and 2-in-\omega). We are interesting in cardinalities of m-in-n families. Cardinalities of open m-in-n families in Baire spaces are studying. In particular, pseudocompact and countably compact spaces are considered.

Date received: February 18, 2000