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On the Topologies of R∞

Published online by Cambridge University Press:  20 November 2018

Chung-Wu Ho
Chung-Wu Ho*
Affiliation:
Department of Mathematics, Statistics and Computer Science, Southern Illinois University at Edwardsville, Edwardsville, Illinois 62026U.S.A.
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Abstract

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Let R∞ be the set of all the finite sequences of real numbers. The author shows that there are uncountably many distinct topologies on the set R∞, each of which coincides with the usual topology when restricted to an Rn. However, under each of these topologies, R∞ is always of the same homotopy type. A generalization to some other spaces is mentioned.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 47 - 51
Copyright
Copyright © Canadian Mathematical Society 1981

References

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3. Whitehead, J. H. C., Combinatorial homotopy I, Bull. Amer. Math. Soc. 55 (1962), 213-245.Google Scholar