# Structure spaces for rings of continuous functions with applications to realcompactifications

Fundamenta Mathematicae (1997)

- Volume: 152, Issue: 2, page 151-163
- ISSN: 0016-2736

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topRedlin, Lothar, and Watson, Saleem. "Structure spaces for rings of continuous functions with applications to realcompactifications." Fundamenta Mathematicae 152.2 (1997): 151-163. <http://eudml.org/doc/212203>.

@article{Redlin1997,

abstract = {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).},

author = {Redlin, Lothar, Watson, Saleem},

journal = {Fundamenta Mathematicae},

keywords = {ring of continuous functions; maximal ideal; ultrafilter; realcompactification; local bounded inversion; Stone-Čech compactification; structure space},

language = {eng},

number = {2},

pages = {151-163},

title = {Structure spaces for rings of continuous functions with applications to realcompactifications},

url = {http://eudml.org/doc/212203},

volume = {152},

year = {1997},

}

TY - JOUR

AU - Redlin, Lothar

AU - Watson, Saleem

TI - Structure spaces for rings of continuous functions with applications to realcompactifications

JO - Fundamenta Mathematicae

PY - 1997

VL - 152

IS - 2

SP - 151

EP - 163

AB - 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).

LA - eng

KW - ring of continuous functions; maximal ideal; ultrafilter; realcompactification; local bounded inversion; Stone-Čech compactification; structure space

UR - http://eudml.org/doc/212203

ER -

## References

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- [5] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer, New York, 1978. Zbl0093.30001
- [6] M. Henriksen, J. R. Isbell and D. G. Johnson, Residue class fields of lattice-ordered algebras, Fund. Math. 50 (1961), 107-117. Zbl0101.33401
- [7] M. Henriksen and D. G. Johnson, On the structure of a class of archimedean lattice-ordered algebras, Fund. Math. 50 (1961), 73-94. Zbl0099.10101
- [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. Zbl0622.54011
- [10] S. Willard, General Topology, Addison-Wesley, Reading, Mass., 1970.

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