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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: 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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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