A common extension of Lindel\"of, H-closed and ccc

The inequality $\mathrm{\mid }X\mathrm{\mid }\le 2^{\chi (X)}$ has been proved to be true for Lindel"of spaces (Arhangel’ski\u\i, 1969), $H$-closed spaces (Dow-Porter, 1982) and ccc spaces (Hajnal-Ju'asz 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.