A common extension of Lindelöf, H-closed and ccc

Abstract

The inequality $|X|\le 2^{\ddot{I}‡(X)}$ has been proved to be true for Lindelöf spaces (Arhangel'ski\uı, 1969), $H$-closed spaces (Dow-Porter, 1982) and ccc spaces (Hajnal-Juász 1967), by quite different arguments. We present a common extension of all these properties which allows us to give a unified proof of these three theorems.