Reducibility, a constructive dual of spatiality

Abstract

An intuitionistic analysis of the relationship between pointfree and pointwise topology brings new notions to light that are hidden from a classical viewpoint. In this paper, we study one of these, namely the notion of reducibility for a pointfree topology, which is classically equivalent to spatiality. We study its basic properties and we relate it to spatiality and to other concepts in constructive topology. We also analyse some notable examples. For instance, reducibility for the pointfree Cantor space amounts to a strong version of Weak König's Lemma.