On the existence of compact metric subspaces with applications to the complementation of $c_{0}$
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- by William H. Chapman and Daniel J. Randtke PDF
- Trans. Amer. Math. Soc. 219 (1976), 133-148 Request permission
Abstract:
A topological space X has property $\sigma - {\text {CM}}$ if for every countable family F of continuous scalar valued functions on X there is a compact metrizable subspace M of X such that $f(X) = f(M)$ for every f in F. Every compact metric space, every weakly compact subset of a Banach space and every closed ordinal space has property $\sigma - {\text {CM}}$. Every continuous image of an arbitrary product of spaces having property $\sigma - {\text {CM}}$ also has property $\sigma - {\text {CM}}$. If X has property $\sigma - {\text {CM}}$, then every copy of ${c_0}$ in $C(X)$ is complemented in $C(X)$. If a locally convex space E belongs to the variety of locally convex spaces generated by the weakly compactly generated Banach spaces, then every copy of ${c_0}$ in E is complemented in E.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 219 (1976), 133-148
- MSC: Primary 54E45; Secondary 46A99
- DOI: https://doi.org/10.1090/S0002-9947-1976-0410688-8
- MathSciNet review: 0410688