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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
DOI: https://doi.org/10.1090/S0002-9939-1984-0722429-5
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

Keywords: Fine homotopy equivalence, countable dimension, property <IMG WIDTH="22" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$C$">, sigma compact linear spaces, Hilbert cube
Article copyright: © Copyright 1984 American Mathematical Society