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), 415428 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), 415428
 MSC: Primary 46E15; Secondary 54A25
 DOI: https://doi.org/10.1090/S00029947197503880621
 MathSciNet review: 0388062