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On the Topologies of R∞
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1981