First countable pseudocompactifications

A general construction for creating first countable pseudo-compact extensions of certain spaces is given. We show that there exists a first countable σ-compact space with no first countable pseudocompactification. We construct a new Suslinean example, namely, a first countable, pseudocompact, ccc, non-separable space. Assuming Martin's Axiom, we can further achieve a point-countable base. A second application is to unify and clarify examples of Scott and Watson of pseudocompact, metaLindelöf and point-countable base non-compact spaces.