Reflecting properties in continuous images of small weight

Abstract

A topological property P is reflected in continuous images of weight at most ω1 if a space X has P whenever every continuous image of X of weight at most ω1 has P. When X is a generalized ordered space, we consider a number of topological properties including feeble Lindelöfness and κ-monolithicity. In the final section we study small images of pseudocompact and countably compact spaces; we give a condition on continuous images of a pseudocompact space in order that it be compact and show that it is consistently true that a countably compact space of countable projective tightness is countably tight.