A remark on linear codimensions of function algebras
We characterize compact sets in the Riemann sphere not separating for which the algebra of all functions continuous on and holomorphic on , restricted to the set , is pervasive on .
In the present note, we characterize the pervasive, analytic, integrity domain and the antisymmetric function algebras respectively, defined on a compact Hausdorff space , in terms of their orthogonal measures on .
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.
In the present note, we characterize the essential set of a function algebra defined on a compact Hausdorff space in terms of its orthogonal measures on .
In the present note, we characterize the essential set of a function algebra defined on a compact Hausdorff space in terms of local properties of functions in at the points off .
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