Geodesic
Function spaces have essential sets
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 337-340.

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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.
Classification : 46E15, 46E35, 46J10
Keywords: compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); its closed subspaces (called function spaces); measure orthogonal to a function algebra or to a function space 
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     author = {\v{C}erych, Jan},
     title = {Function spaces have essential sets},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {337--340},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
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     mrnumber = {1651963},
     zbl = {0937.46048},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1998__39_2_a9/}
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Čerych, Jan. Function spaces have essential sets. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 337-340. http://geodesic.mathdoc.fr/item/CMUC_1998__39_2_a9/