ITES2001 Fourth Italian-Spanish conference on General Topology and its applications Bressanone, 27-30 June 2001

Cosimo Guido, Ljubiša D.R. Kočinac

A new selection principle

Dipartimento di Matematica, Università di Lecce, Italy

We introduce and study the following new selection principle. Let X be a topological space and let A and B denote collections whose elements are families of (open) subsets of X.

Then S_{pf}(A, B) denotes that for each sequence (U_{n} : n ∈ ℕ) of elements of A there is a sequence (V_{n} : n ∈ ℕ) such that for each n V_{n} is a point-finite family with V_{n} < U_{n} and ⋃_{n∈ℕ} V_{n} ∈ B.

This general selection principle is compared with other well known principles and it is investigated in relation with metacompactness and other topological properties.

2000 Mathematics Subject Classification: 54D20, 54D45.