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Can partial indexings be totalized?

Published online by Cambridge University Press:  12 March 2014

Dieter Spreen
Dieter Spreen*
Affiliation:
Fachbereich Mathematik, Theoretische Informatik, Universität Siegen, 57068 Siegen, Germany, E-mail: spreen@informatik.uni-siegen.de
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Abstract

In examples like the total recursive functions or the computable real numbers the canonical indexings are only partial maps. It is even impossible in these cases to find an equivalent total numbering. We consider effectively given topological T0-spaces and study the problem in which cases the canonical numberings of such spaces can be totalized, i.e., have an equivalent total indexing. Moreover, we show under very natural assumptions that such spaces can effectively and effectively homeomorphically be embedded into a totally indexed algebraic partial order that is closed under the operation of taking least upper bounds of enumerable directed subsets.

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1157 - 1185
Copyright
Copyright © Association for Symbolic Logic 2001

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