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Can Partial Indexings Be Totalized?

Dieter Spreen
The Journal of Symbolic Logic
Vol. 66, No. 3 (Sep., 2001), pp. 1157-1185
DOI: 10.2307/2695099
Stable URL: http://www.jstor.org/stable/2695099
Page Count: 29
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Can Partial Indexings Be Totalized?
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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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