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CCA
2005
Springer
13 years 6 months ago
Computable Versions of Basic Theorems in Functional Analysis
If one wishes to find out whether a computational problem over discrete data is solvable or how complex it is, the classical approach is to represent the discrete objects in quest...
Atsushi Yoshikawa, Mariko Yasugi
CCA
2005
Springer
13 years 10 months ago
Effectively Open Real Functions
A function f is continuous iff the pre-image f −1[V ] of any open setV is open again. Dual to this topological7 property, f is called open iff the image f [U] of any open set U ...
Martin Ziegler
CCA
2005
Springer
13 years 10 months ago
A Lambda Calculus for Real Analysis
Abstract Stone Duality is a revolutionary theory that works directly with computable continuous functions, without using set theory, infinitary lattice theory or a prior theory o...
Paul Taylor 0002
CCA
2005
Springer
13 years 10 months ago
Representing Probability Measures using Probabilistic Processes
In the Type-2 Theory of Effectivity, one considers representations of topological spaces in which infinite words are used as “names” for the elements they represent. Given s...
Matthias Schröder, Alex K. Simpson
CCA
2005
Springer
13 years 10 months ago
Randomness and Universal Machines
Santiago Figueira, Frank Stephan, Guohua Wu