Two More Hereditarily Separable Non-Lindelöf Spaces

Abstract

Our method usingCHis a blend of two earlier constructions (Hajnal-Juhász [2] and Ostaszewski [4]) of hereditarily separable(HS),regular, non-Lindelöf, first countable spaces. [4] produces a much better space than ours in § 1 ; it has all of our properties except that it is not realcompact (which is probably more interesting), and it is countably compact as well; however, the construction works only under ◇, which implies the continuum hypothesis(CH)but is not equivalent to it.