Categorical Completeness: Surprises and Difficulties
by
Bruce S. Burdick
Roger Williams University

It is possible for a category, with a notion of embedding, to define what the complete objects should be. Complete spaces, for the category of T₀ uniform spaces, and sober spaces, for the category of T₀ spaces, are two notions of complete object which arise in this way. We survey some of what is known about this, and describe an interesting but ultimately unsuccessful attempt to apply this approach in an asymmetric way to bitopological spaces.

Date received: April 17, 2002