# Function spaces have essential sets

Commentationes Mathematicae Universitatis Carolinae (1998)

- Volume: 39, Issue: 2, page 337-340
- ISSN: 0010-2628

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topČerych, Jan. "Function spaces have essential sets." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 337-340. <http://eudml.org/doc/248268>.

@article{Čerych1998,

abstract = {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.},

author = {Čerych, Jan},

journal = {Commentationes Mathematicae Universitatis Carolinae},

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; compact Hausdorff space; sup-norm algebra; function algebras; function spaces; orthogonal measure},

language = {eng},

number = {2},

pages = {337-340},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Function spaces have essential sets},

url = {http://eudml.org/doc/248268},

volume = {39},

year = {1998},

}

TY - JOUR

AU - Čerych, Jan

TI - Function spaces have essential sets

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1998

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 39

IS - 2

SP - 337

EP - 340

AB - 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.

LA - eng

KW - 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; compact Hausdorff space; sup-norm algebra; function algebras; function spaces; orthogonal measure

UR - http://eudml.org/doc/248268

ER -

## References

top- Bear H.S., Complex function algebras, Trans. Amer. Math. Soc. 90 (1959), 383-393. (1959) Zbl0086.31602MR0107164
- Hoffman K., Singer I.M., Maximal algebras of continuous functions, Acta Math. 103 (1960), 217-241. (1960) Zbl0195.13903MR0117540
- Glicksberg I., Measures orthogonal to algebras and sets of antisymmetry, Trans. Amer. Math. Soc. 98 (1962), 415-435. (1962) Zbl0111.11801MR0173957
- Čerych J., On essential sets of function algebras in terms of their orthogonal measures, Comment. Math. Univ. Carolinae 36.3 (1995), 471-474. (1995) MR1364487

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