Topology Proceedings
Document # baak-13
Electronic Version 24 Summer (1999) |
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Countably generated intermediate algebras between C*(X) and C(X)
Jesús M. Domínguez and J. Gómez-Pérez
Let X be a completely regular space. We study those intermediate algebras between C*(X) and C(X) that are obtained by adjoining to C*(X) a countable family of unbounded functions in C(X). We shall call them countably generated intermediate algebras, and they are exactly the intermediate algebras that have a countable cofinal subset consisting of unbounded functions. They are far away from being isomorphic to any C(T). In fact we show that no countably generated intermediate algebra is closed under composition with functions in C(R). We also examine a classical intermediate algebra of real sequences, previously studied by R.M. Brooks and D. Plank, in order to show that it is not countably generated over C*(N).
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Date published electronically: March 5, 2001.