The compactifications to which an element of $C^{\ast } (X)$ extends
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- by Richard E. Chandler and Ralph Gellar PDF
- Proc. Amer. Math. Soc. 38 (1973), 637-639 Request permission
Abstract:
We first determine a necessary and sufficient condition for a function $f \in {C^\ast }(X)$, which extends to a compactification of $X$, to extend to a smaller compactification. We apply this result to show that when $|\beta X\backslash X| \leqq {\aleph _0}$ there is an $f \in {C^\ast }(X)$ which extends to no compactification other than $\beta X$. Two examples show that when ${\aleph _0} < |\beta X\backslash X| \leqq c$ no such definite result may be obtained.References
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199, DOI 10.1007/978-1-4615-7819-2
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 637-639
- MSC: Primary 54D35
- DOI: https://doi.org/10.1090/S0002-9939-1973-0314003-2
- MathSciNet review: 0314003