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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the structure of $S$ and $C(S)$ for $S$ dyadic
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by James Hagler PDF
Trans. Amer. Math. Soc. 214 (1975), 415-428 Request permission

Abstract:

A dyadic space S is defined to be a continuous image of ${\{ 0,1\} ^\mathfrak {m}}$ for some infinite cardinal number $\mathfrak {m}$. We deduce Banach space properties of $C(S)$ and topological properties of S. For example, under certain cardinality restrictions on $\mathfrak {m}$, we show: Every dyadic space of topological weight $\mathfrak {m}$ contains a closed subset homeomorphic to ${\{ 0,1\} ^\mathfrak {m}}$. Every Banach space X isomorphic to an $\mathfrak {m}$ dimensional subspace of $C(S)$ (for S dyadic) contains a subspace isomorphic to ${l^1}(\Gamma )$ where $\Gamma$ has cardinality $\mathfrak {m}$.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 214 (1975), 415-428
  • MSC: Primary 46E15; Secondary 54A25
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0388062-1
  • MathSciNet review: 0388062