Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and representations closer, unify some terminology, simplify some technical details, suggest interesting open questions and new invariants of topological spaces rele...

We give more properties and applications to the class of somewhat nearly continuous functions introduced by Piotrowski. Among applications, we show that Baire property is preserved under quasiopen injection images spaces are countable fiber complete preimages. The later statement generalizes results given Noll, Mirmostafaee

Abstract We show that for a given initial point the typical, in sense of Baire category, nonexpansive compact valued mapping F has following properties: there is unique sequence successive approximations and this converges to fixed . In case separable Banach spaces we typical residual set points have trajectory.