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

Stable maps into the Hilbert cube


Authors: Dennis J. Garity and Dale M. Rohm
Journal: Proc. Amer. Math. Soc. 104 (1988), 632-634
MSC: Primary 57N20; Secondary 54F45, 54H25, 55M10
MathSciNet review: 962840
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Abstract: A map into the Hilbert cube is stable if each composition with projection onto a finite number of factors is stable. We prove that a map from a compact metric space into the Hilbert cube is stable if and only if it is universal. As a consequence, the composition of a stable map with any self homeomorphism of the Hilbert cube is also stable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0962840-4
PII: S 0002-9939(1988)0962840-4
Keywords: Stable map, essential map, universal map, essential family, strongly infinite dimensional
Article copyright: © Copyright 1988 American Mathematical Society