Biframes

Abstract

<p>Biframes and their homomorphisms are the subject of this thesis. Various traditional notions from topology and frame theory are extended to this setting: compactness, regularity, normality, zero-dimensionality, Booleanness, coherence, super-coherence, continuity, supercontinuity and connectedness. The category of biframes is shown to be complete and cocomplete, and its monomorphisms, epimorphisms and projectives characterized. Of particular importance are the compactifications--their correspondence with strong inclusions, the existence of zero-dimensional ones and of least ones, and their relations to rim-compactness and normality.</p>