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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Property $ C$ and fine homotopy equivalences


Authors: Jan van Mill and Jerzy Mogilski
Journal: Proc. Amer. Math. Soc. 90 (1984), 118-120
MSC: Primary 54F45; Secondary 55P10
MathSciNet review: 722429
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that within the class of metric $ \sigma $-compact spaces, proper fine homotopy equivalences preserve property $ C$, which is a slight generalization of countable dimensionality. We also give an example of an open fine homotopy equivalence of a countable dimensional space onto a space containing the Hilbert cube.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722429-5
PII: S 0002-9939(1984)0722429-5
Keywords: Fine homotopy equivalence, countable dimension, property $ C$, sigma compact linear spaces, Hilbert cube
Article copyright: © Copyright 1984 American Mathematical Society