Dense sigma-compact subsets of infinite-dimensional manifolds

Chapman, T. A.

doi:10.1090/S0002-9947-1971-0283828-7

Dense sigma-compact subsets of infinite-dimensional manifolds
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by T. A. Chapman

Trans. Amer. Math. Soc. 154 (1971), 399-426

DOI: https://doi.org/10.1090/S0002-9947-1971-0283828-7

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Abstract:

In this paper four classes of separable metric infinite-dimensional manifolds are studied; those which are locally the countable infinite product of lines, those which are locally open subsets of the Hubert cube, and those which are locally one of two dense sigma-compact subsets of the Hilbert cube. A number of homeomorphism, product, characterization, and embedding theorems are obtained concerning these manifolds.

References

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A characterization of apparent boundaries of the Hilbert cube

16

On sigma-compact subsets of infinite-dimensional spaces

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Topologie

Espaces métrisables, espaces complets

10

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