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1997 | 152 | 2 | 151-163
Tytuł artykułu

Structure spaces for rings of continuous functions with applications to realcompactifications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).
Rocznik
Tom
152
Numer
2
Strony
151-163
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-03-07
poprawiono
1996-08-20
Twórcy
  • Department of Mathematics, The Pennsylvania State University, Abington, Pennsylvania 19001, U.S.A., lhr5@psu.edu
  • Department of Mathematics, California State University, Long Beach, California 90840, U.S.A., saleem@csulb.edu
Bibliografia
  • [1] W. Adamski, Two ultrafilter properties for vector lattices of real-valued functions, Publ. Math. Debrecen 45 (1994), 225-267.
  • [2] R. M. Brooks, A ring of analytic functions, Studia Math. 24 (1964), 191-210.
  • [3] H. L. Byun, L. Redlin and S. Watson, Local invertibility in subrings of C*(X), Bull. Austral. Math. Soc. 46 (1992), 449-458.
  • [4] H. L. Byun and S. Watson, Prime and maximal ideals in subrings of C(X), Topology Appl. 40 (1991), 45-62.
  • [5] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer, New York, 1978.
  • [6] M. Henriksen, J. R. Isbell and D. G. Johnson, Residue class fields of lattice-ordered algebras, Fund. Math. 50 (1961), 107-117.
  • [7] M. Henriksen and D. G. Johnson, On the structure of a class of archimedean lattice-ordered algebras, Fund. Math. 50 (1961), 73-94.
  • [8] D. Plank, On a class of subalgebras of C(X) with applications to βX, Fund. Math. 64 (1969), 41-54.
  • [9] L. Redlin and S. Watson, Maximal ideals in subalgebras of C(X), Proc. Amer. Math. Soc. 100 (1987), 763-766.
  • [10] S. Willard, General Topology, Addison-Wesley, Reading, Mass., 1970.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv152i2p151bwm
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