Selective separability and products
by
Liljana Babinkostova
Boise State University

The classical notion of separability of a topological space can be strengthened in several ways. One strengthening is called selective separability: For each

sequence of dense sets one can choose a new dense set by selecting finitely many points from each of the given dense sets.

Even nice separable spaces need not be selectively separable. We present a CH example that the product of two selectively separable spaces need not be

selectively separable. This answers two recent questions by A. Bella et al.

Date received: March 20, 2008