Previous |  Up |  Next

Article

Keywords:
proper uniform algebra; Hausdorff space
Summary:
In this brief note, we see that if $A$ is a proper uniform algebra on a compact Hausdorff space $X$, then $A$ is flat.
References:
[1] Michael, E., Pełczyński, A.: A linear extension theorem. Illinois J. Math. 11 (1967), 563-579. MR 0217582
[2] Nyikos, P., Schäffer, J. J.: Flat spaces of continuous functions. Studia Math. 42 (1972), 221-229. MR 0308761
[3] Pełczyński, A.: Some linear topological properties of separable function algebras. Proc. Amer. Math. Soc. 18 (1967), 652-660. DOI 10.2307/2035434 | MR 0213883
[4] Schäffer, J. J.: Geometry of spheres in normed spaces, Lecture Notes in Pure and Applied Mathematics, No. 20. Marcel-Dekker, Inc., New York-Basel (1976). MR 0467256
[5] Rudin, W.: Continuous functions on compact spaces without perfect subsets. Proc. Amer. Math. Soc. 8 (1957), 39-42. DOI 10.1090/S0002-9939-1957-0085475-7 | MR 0085475 | Zbl 0077.31103
Partner of
EuDML logo