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Transactions of the American Mathematical Society

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Perfect open and distinguishable multivalued maps

Author: Eric John Braude
Journal: Trans. Amer. Math. Soc. 182 (1973), 431-441
MSC: Primary 54C50; Secondary 54H05
MathSciNet review: 0334137
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Abstract: It is shown that perfect open multivalued maps preserve $ \mathcal{Z}$-analytic sets (which include compact zero sets) as well as other objects of descriptive set theory. The concept of ``distinguishability", introduced by Frolík, is applied to multivalued maps, yielding a new class of such maps with similar preservation properties.

That the projection of a compact zero set is a zero set is one corollary, and another is a generalized $ {\mathcal{G}_\delta }$ diagonal metrization theorem.

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Keywords: Perfect, open maps, distinguishable, multivalued maps, $ \mathcal{Z}$-analytic sets, descriptive set theory, $ {\mathcal{G}_\delta }$ diagonal, projection, Baire, zero sets, Borel sets, analytic sets, Souslin
Article copyright: © Copyright 1973 American Mathematical Society

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