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