Simultaneous extensions from discrete subspaces
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- by H. Banilower PDF
- Proc. Amer. Math. Soc. 36 (1972), 451-455 Request permission
Abstract:
If N is a denumerable, discrete, normally embedded subspace of the completely regular space S, then any bounded linear operator from $C(N)$ into $C(S)$ that extends functions in ${C_0}(N)$ necessarily extends all bounded functions on some infinite subset of N (that are zero elsewhere on N). For compact S, such operators exist whenever $C(S)$ contains a subspace isometric to (m). It is also shown, assuming the continuum hypothesis, that if S is a locally compact F-space and ${C_0}(S)$ is complemented in $C(S)$, then S is countably compact.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 451-455
- MSC: Primary 53C20; Secondary 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0319138-5
- MathSciNet review: 0319138