Abstract
We introduce a new equivalence relation of Tykhonoff spaces. By definition, two Tykhonoff spaces X and Y are in this relation if some strictly 0-sufficient subsets A in Cp(X) and B in Cp(Y) are homeomorphic and this homeomorphism has the weak finite support property. We show that the classification of function spaces on ordinals up to homeomorphisms with weak finite support property coincides with one up to uniform homeomorphisms. As a consequence we obtain that there exists a homeomorphism of function spaces on ordinals which has the weak support property and which cannot be replaced by linear one.
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