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On the dissonance of some metrizable spaces

✍ Scribed by C. Costantini; S. Watson

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
657 KB
Volume
84
Category
Article
ISSN
0166-8641

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✦ Synopsis

We prove that for every separable, O-dimensional me&able space X without isolated points, such that every compact subset of it is scattered, the cocompact topology on the hyperspace of X does not coincide with the upper Kuratowski topology-that is, X is dissonant. In particular, it follows that the rational line is dissonant, and that there exist dissonant, hereditarily Baire, separable metrizable spaces.

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