Remote filters and discretely generated spaces

Abstract

Alas, Junqueira and Wilson asked whether there isa discretely generated locally compact space whose one pointcompactification is not discretely generated and gave a consistentexample using CH. Their construction uses a remote filter in$\omega \times {}^{\omega }2$ with a base of order type ${\omega }_1$ when ordered modulocompact subsets. In this paper we study the existence andpreservation (under forcing extension) of similar types offilters, mainly using small uncountable cardinals. With theseresults we show that the CH example can be constructed in moregeneral situations.