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Immersions of Metric Spaces into Euclidean Spaces
Published online by Cambridge University Press: 20 November 2018
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In a recent paper on isotopy invariants (1), S. T. Hu denned the enveloping space Em(X) of any given topological space X for each integer m > 1. By an application of the Smith theory to the singular cohomology of the enveloping space Em(X), he obtained his immersion classes for every n = 1, 2, 3, . . . and proved (3) the main theorem that a necessary condition for a compact metric space X to be immersible into the ^-dimensional Euclidean space Rn is
. This theorem was proved earlier by W. T. Wu (4) for finitely triangulable spaces X using purely combinatorial methods.
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- Copyright © Canadian Mathematical Society 1965