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Integer-Valued Continuous Functions II

Published online by Cambridge University Press:  20 November 2018

H. Subramanian
H. Subramanian*
Affiliation:
State University of New York, Amherst, New York
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We follow [6] and [7] for all terminologies. The purpose of this note is to prove

Theorem 1. Let X and Y be any two integer-compact spaces. The following are equivalent:

  1. (1) X is homeomorphic to Y.

  2. (2) C(X, Z) and C(Y, Z) are isomorphic as rings.

  3. (3) C(X, Z) and C(F, Z) are isomorphic as lattices.

  4. (4) C(X, Z) and C(Y, Z) are isomorphic as p.o. groups.

  5. (5) C(X, Z) and C(Y, Z) are isomorphic as multiplicative semigroups.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 235 - 237
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Ailing, N. L., Rings of continuous integer-valued functions and nonstandard arithmetic, Trans. Amer. Math. Soc. 118 (1965), 498-525.Google Scholar
2. Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand, Princeton, N.J., 1960.Google Scholar
3. Henriksen, M., On the equivalence of the ring, lattice, and semi-group of continuous functions, Proc. Amer. Math. Soc. 7 (1956), 959-960.Google Scholar
4. Kist, J., Minimal prime ideals in commutative semigroups, Proc. London Math. Soc. 13 (1963), 31-50.Google Scholar
5. Shirota, T., A generalization of a theorem of I. Kaplansky, Osaka J. Math. 4 (1952), 121-132.Google Scholar
6. Subramanian, H., Kaplansky's theorem for f-rings, Math. Ann. 179 (1968), 70-73.Google Scholar
7. Subramanian, H., Integer-valued continuous functions, Bull. Soc. Math. France 97 (1969).Google Scholar