Remote Filters and Discretely Generated Spaces

摘要

Alas, Junqueira and Wilson asked whether there is a discretely generatedlocally compact space whose one point compactification is not discretelygenerated and gave a consistent example using CH. Their construction uses aremote filter in $\omega\times{}^{\omega}2$ with a base of order type$\omega_1$ when ordered modulo compact subsets. In this paper we study theexistence and preservation (under forcing extension) of similar types offilters, mainly using small uncountable cardinals. With these results we showthat the CH example can be constructed in more general situations.