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Integer-Valued Continuous Functions II
Published online by Cambridge University Press: 20 November 2018
Extract
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) X is homeomorphic to Y.
(2) C(X, Z) and C(Y, Z) are isomorphic as rings.
(3) C(X, Z) and C(F, Z) are isomorphic as lattices.
(4) C(X, Z) and C(Y, Z) are isomorphic as p.o. groups.
(5) C(X, Z) and C(Y, Z) are isomorphic as multiplicative semigroups.
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- Copyright © Canadian Mathematical Society 1971
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