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.**