Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Projecting $ C(S)$ onto $ C\sb{0}(S)$

Author: H. Banilower
Journal: Proc. Amer. Math. Soc. 33 (1972), 349-354
MSC: Primary 46E10; Secondary 54C35
MathSciNet review: 0295062
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E10, 54C35

Retrieve articles in all journals with MSC: 46E10, 54C35

Additional Information

Keywords: Uncomplemented in $ C(S)$, simultaneous extension, denumerable discrete subspace, basically disconnected, extremally disconnected
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society