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Axiomatic method of partitions in the theory of Nöbeling spaces. III: Consistency of the axiom system. (English. Russian original) Zbl 1148.54018
Sb. Math. 198, No. 7, 909-934 (2007); translation from Mat. Sb. 198, No. 7, 3-30 (2007).
This is the third part of a series of three papers in which the author proves the following classical conjecture on a characterization of Nöbeling spaces.
Theorem. For every $$2 \leq k < \infty$$, if a strongly $$k$$-universal $$k$$ dimensional Polish space is an absolute extensor in dimension $$k$$, then it is homeomorphic to the $$k$$ dimensional Nöbeling space $$N_{k}^{2k+1}$$.
For the definitions, we refer to the review of the first part, see S. M. Ageev [Sb. Math. 198, No. 3, 299–342 (2007; Zbl 1147.54019); translation from Mat. Sb. 198, No. 3, 3–50 (2007)].
In the first two parts of the series, the author introduced the axiom system of Nöbeling spaces, and reduced the theorem above to the proof of the consistency of this axiom system. The present last part contains the final step, i.e. that the so-called Nöbeling cores of constructible manifolds satisfy the axiom system of Nöbeling spaces.

##### MSC:
 54F65 Topological characterizations of particular spaces 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
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