Admissible representations of effective cpo's

Two categories of effective continuous cpos

This paper presents two categories of effective continuous cpos. We define a new criterion on the basis of a cpo as to make the resulting category of consistently complete continuous cpos cartesian closed. We also generalise the definition of a complete set, used as a definition of effective bifinite domains in [HSH02], and investigate what closure results that can be obtained.

Admissible Representations of Probability Measures

In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type-2 Theory of Effectivity. This gives rise to a natural representation of the set M(X) of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel pro...

5 Admissible Semi - Linear Representations

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described. Let k be a field of characteristic zero containing all ℓ-primary roots of unity for a prime ℓ, F...

Admissible representations for continuous computations

Admissible Domain Representations of Topological Spaces

In this paper we consider admissible domain representations of topological spaces. A domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to D via a continuous function from E to D. We present a characterisation theorem of when a topological space has a λ-admissible and κ-based domain representation. We also prove ...