Projecting $C(S)$ onto $C_{0}(S)$
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- by H. Banilower PDF
- Proc. Amer. Math. Soc. 33 (1972), 349-354 Request permission
Abstract:
If a locally compact Hausdorff space S has a denumerable discrete closed subspace N for which there exists a simultaneous extension E from $C(N)$ into $C(S)$ satisfying $E({C_0}(N)) \subset {C_0}(S)$, then ${C_0}(S)$ is uncomplemented in $C(S)$. This holds whenever (i) S is not pseudocompact, or (ii) S is not countably compact and is a subspace of a basically disconnected space.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 349-354
- MSC: Primary 46E10; Secondary 54C35
- DOI: https://doi.org/10.1090/S0002-9939-1972-0295062-1
- MathSciNet review: 0295062