On the weak finite support property of homeomorphisms of function spaces on ordinals V. Lazarev
Material type:
ArticleContent type: Текст Media type: электронный Subject(s): функциональные пространства | ординалы | топология поточечной сходимости | гомеоморфизмGenre/Form: статьи в журналах Online resources: Click here to access online
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Topology and its applications Vol. 275. P. 107012 (1-8)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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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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