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A note on pervasive algebras. (English) Zbl 0602.46057
We prove the following theorem:
Let A be a pervasive algebra on X. Let F and H be a disjoint couple of closed subsets of X which both have nonvoid interiors. Suppose that there is a constant c with the following property: Whenever e is positive, then there is an f in A satisfying \[ | f|_ F<e,\quad | f- 1|_ H<e,\quad | f| \leq c. \] Then A is equal to C(X).

46J10 Banach algebras of continuous functions, function algebras
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