Bitopological spaces

A bitopological space (X,τ,μ) is a set X with two topologies. The study of bitopological spaces was initiated by J. C. Kelly.

In this thesis, we study pairwise-separation axioms as defined by J. C. Kelly, C. W. Patty, and F. P. Lane. In addition, definitions for semi-compactness, semi-paracompactness, and bicontinuous functions are proposed and are related to the definitions of pairwise-separated spaces.

Finally, quasi-pseudo-metric spaces are defined, and a number of quasi-pseudo-metrization theorems are summarized.