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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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- Research Article
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- Copyright © Canadian Mathematical Society 1965
References
1.
Hu, S. T., Isotopy invariants 0﹜topological spaces, Proc. Roy. Soc. London, Ser. A, 255 (1960), 331–366.Google Scholar
2.
Hu, S. T., Smith invariants in singular cohomology, Hung-Ching Chow 60th Anniversary Vol. (1962), Inst, of Math., Acad. Sinica, Taipei, 1-17.Google Scholar
3.
Hu, S. T., Immersions of compact metric spaces into Euclidean spaces, Illinois J. Math., 7 (1963), 415–424.Google Scholar
4.
Wu, W. T., On the realization of complexes in Euclidean spaces
11, Acta Math. Sinica, 7 (1957), 79–101.Google Scholar
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