Hyperspaces of nowhere topologically complete spaces |
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Authors: | T Banakh R Cauty |
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Institution: | (1) Lvov University, Lvov, USSR;(2) Université Paris VI, Paris, France |
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Abstract: | It is proved that ifX is a connected locally continuumwise connected coanalytic nowhere topologically complete space, then the hyperspace 2
X
of all nonempty compact subsets ofX is strongly universal in the class of all coanalytic spaces. Moreover, 2
X
is homeomorphic to Π2 ifX is a Baire space, and toQ∖Π1 ifX contains a dense absoluteG
δ-setG ⊂X such that the intersectionG ∩U is connected for any open connectedU ⊂X. (Here Π1, Π1⊂X are the standard subsets of the Hilbert cubeQ absorbing for the classes of analytic and coanalytic spaces, respectively.) Similar results are obtained for higher projective
classes.
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 35–51, July, 1997.
Translated by O. V. Sipacheva |
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Keywords: | hyperspace connected locally continuumwise connected space nowhere topologically complete space coanalytic space Z-set absoluteG δ absolute retract meager space |
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