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

Abstract

In this paper we provide some general results about topological spaces X which satisfy starn- P , weakly starn- P and almost starn- P, for P∈ { κ ᴄᴄ , W κ L , ᴅ κ ᴄᴄ } , where κ is an infinite cardinal number. The particular cases when κ = ω , P ∈ { ᴄᴄᴄ , weakly Lindelöf , ᴅ ᴄᴄᴄ } are obtained. Furthermore, for the same classes of spaces defined by such P, by applying Erdős-Radó's theorem and using the rank l-diagonal notion, we establish some cardinal inequalities.

Keywords

• cardinality
• covering
• rank l-diagonal
• star-p spaces
• weakly (almost) star-ccc spaces
• weakly (almost) star-dccc spaces
• weakly (almost) star-weakly lindelöf spaces