Journal of Applied Analysis 01 (1995), No. 2, 181--204
Copyright Heldermann Verlag 1995
Coinitial Families of Perfect Sets
Marek Balcerzak
Institute of Mathematics, Technical University, Al. Politechniki 11, 90-924 Lodz, Poland
Andrzej Roslanowski
Mathematical Institute, Wroclaw University, Pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Let Perf(X) denote the family of all perfect subsets of a perfect Polish space X. We show several properties and characterizations of coinitial subfamilies of Perf (X). Connections with the Vietoris topology and Morgan's category bases are observed. We characterize the least cardinality of a family of coinitial ideals with noncoinitial intersection. Some examples of special noncoinitial families in Perf (X) are presented. Much place is devoted to perfect isomorphisms between ideals of subsets of X.
Keywords: Polish space, perfect set, s0-set, coinitial set, ideal of sets, isomorphism of ideals, category base, Vietoris topology, Sacks Amoeba forcing.
MSC: 28A05, 06A07, 04A15, 54E50, 54H05, 54B20
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