This book is an introduction to constructive mathematics with an emphasis on techniques
and results obtained in the last twenty years. The text covers fundamental theory of the real …

Constructive mathematics is distinguished from its traditional counterpart, classical
mathematics, by the strict interpretation of the phrase “there exists” as “we can construct”. In …

The theory of Bishop spaces (TBS) is so far the least developed approach to constructive
topology with points. Bishop introduced function spaces, here called Bishop spaces, in …

Uniform sequential continuity, a property classically equivalent to sequential continuity on
compact sets, is shown, constructively, to be a consequence of strong continuity on a metric …

We extend Bishopʼs concept of function spaces to the concept of pre-function spaces. We
show that there is an adjunction between the category of neighbourhood spaces and the …

We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We
show that there is an adjunction between the category of quasi-apartness spaces and the …

The notion of apartness has recently shown promise as a means of lifting constructive
topology from the restrictive context of metric spaces to more general settings. Starting from …

We defend pluralism in mathematics, and in particular Errett Bishop's constructive approach
to mathematics, on pragmatic grounds, avoiding the philosophical issues which have …

Apartness spaces were introduced as a constructive counterpart to proximity spaces which,
in turn, aimed to model the concept of nearness of sets in a metric or topological …

An existential statement seems to admit of a constructive proof without countable choice only
if the object to be constructed is uniquely determined, or is intended as an approximate …