Polish spaces, computer approximation, and cocompact quasimetrizability


Krzysztof Ciesielski & R. C. Flagg & Ralph Kopperman

Topology Appl. 119(3) (2002), 241--256.

Answering a question of J. Lawson (formulated also earlier, in 1984, by Kamimura and Tang) we show that every Polish space admits a bounded complete computational model. This results from our construction, in each polish space (X,T), of a countable family C of closed subsets of X such that:

(cp) each subset of C with the finite intersection property has nonempty intersection;

(br) the interiors int(C) of all C in C form a base for X;

(r*) for every C in C and x in X\C there is a D in C such that C is a subset of int(D) and x is not in D.

These conditions assure us that there is another compact topology T* on X weaker than T such that the bitopological space (X,T,T*) is pairwise regular. The existence of such a topology is also shown equivalent to admitting a bounded complete computational model.

Compare also the paper Characterizing topologies with bounded complete computational models by the authors.

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Last modified March 5, 2002.