Projective versions of the properties in the Scheepers Diagram

Abstract

Let P be a topological property. A.V. Arhangel'skii calls X projectively P if every second countable continuous image of X is P. Lj.D.R. Kočinac characterized the classical covering properties of Menger, Rothberger, Hurewicz and Gerlits-Nagy in term of continuous images in R ω . In this paper we have gave the functional characterizations of all projective versions of the selection properties in the Scheepers Diagram.Theorem 14.2. For a s-space X with iw(X) = ω, the following statements are equivalent:

The projectively Hurewicz property is t-invariant

“…Characterizations of the classical covering properties in terms a selection principle restricted to countable covers by cozero sets are given in [4]. In [7,8] we obtained the functional characterizations of all projective versions of the selection properties in the Scheepers Diagram.…”