Robert Kenny - Effective zero-dimensionality for computable metric spaces

lmcs:1023 - Logical Methods in Computer Science, March 25, 2015, Volume 11, Issue 1 - https://doi.org/10.2168/LMCS-11(1:11)2015
Effective zero-dimensionality for computable metric spaces

Authors: Robert Kenny ORCID-iD

    We begin to study classical dimension theory from the computable analysis (TTE) point of view. For computable metric spaces, several effectivisations of zero-dimensionality are shown to be equivalent. The part of this characterisation that concerns covering dimension extends to higher dimensions and to closed shrinkings of finite open covers. To deal with zero-dimensional subspaces uniformly, four operations (relative to the space and a class of subspaces) are defined; these correspond to definitions of inductive and covering dimensions and a countable basis condition. Finally, an effective retract characterisation of zero-dimensionality is proven under an effective compactness condition. In one direction this uses a version of the construction of bilocated sets.


    Volume: Volume 11, Issue 1
    Published on: March 25, 2015
    Accepted on: June 25, 2015
    Submitted on: November 9, 2013
    Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science

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