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Let C(X, I) denote the semigroup of continuous functions from the topological space X to I = [0, 1], equipped with the pointwise multiplication. The paper studies semigroup homomorphisms C(Y, I) -> C(X, I), with emphasis on isomorphisms. The crucial observation is that, in this setting, homomorphisms preserve order, so isomorphisms preserve order in both directions and they are automatically lattice isomorphisms. Applications to uniformly continuous and Lipschitz functions on metric spaces are given. Sample...
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Citation Formats
Y. Ozan, “Seminar Notes on Arf Invariant,” 2016, Accessed: 00, 2021. [Online]. Available: http://users.metu.edu.tr/ozan/arf2016.pdf.
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