Constructive maximal point spaces
by
Mike Smyth
Imperial College, London

We re-examine Martin-Lo"f's (1970) constructive maximality definition in the setting of R-structures (=abstract bases, in A. Jung's terminology). The constructive maximal points do not in general coincide with the classical ones (even classically), and this sheds some light on the Lawson Condition. A second topic of recent interest which we consider is (partial) metrizability. The ideas can be used to define, in an arbitrary omega-continuous poset, weight and distance functions with good properties, but these do not in general amount to a pmetric. If time permits, I may also describe some recent work (with R. Tsaur) on hyperconvex semi-metric spaces.

Date received: April 18, 2002