Some results on weaker forms of starn-CCC, weakly Lindelöf and starn-DCCC spaces

Abstract

[EN] In this paper we provide some general results about topological spaces X satisfying any of the following properties: starn-P, weakly starn-P or almost starn-P, for P ∈ {κcc, WκL, dκcc}, where κ is an infinite cardinal number. The particular cases when κ = ω, P ∈ {ccc, weakly Lindel¨of, dccc} are obtained. Furthermore, for the same classes of spaces defined by such P, by applying Erd˝os-Rad´o’s theorem and using the rank l-diagonal notion, we establish some cardinal inequalities.