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Function spaces have essential sets

Jan Čerych — 1998

Commentationes Mathematicae Universitatis Carolinae

It is well known that any function algebra has an essential set. In this note we define an essential set for an arbitrary function space (not necessarily algebra) and prove that any function space has an essential set.

Pervasive algebras on planar compacts

Jan Čerych — 1999

Commentationes Mathematicae Universitatis Carolinae

We characterize compact sets X in the Riemann sphere 𝕊 not separating 𝕊 for which the algebra A ( X ) of all functions continuous on 𝕊 and holomorphic on 𝕊 X , restricted to the set X , is pervasive on X .

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