Simultaneous extensions from discrete subspaces

Author:
H. Banilower

Journal:
Proc. Amer. Math. Soc. **36** (1972), 451-455

MSC:
Primary 53C20; Secondary 46E15

MathSciNet review:
0319138

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Abstract | References | Similar Articles | Additional Information

Abstract: If *N* is a denumerable, discrete, normally embedded subspace of the completely regular space *S*, then any bounded linear operator from into that extends functions in necessarily extends all bounded functions on some infinite subset of *N* (that are zero elsewhere on *N*). For compact *S*, such operators exist whenever contains a subspace isometric to (*m*). It is also shown, assuming the continuum hypothesis, that if *S* is a locally compact *F*-space and is complemented in , then *S* is countably compact.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0319138-5

Keywords:
Simultaneous extension,
discrete subspace,
*F*-space,
subspace isometric to (*m*)

Article copyright:
© Copyright 1972
American Mathematical Society