HOMOMORPHISMS BETWEEN C(X) AND C(Y)

Hazra, S and Basila, P (2022) HOMOMORPHISMS BETWEEN C(X) AND C(Y). In: Mathematics Student, 91 (3-4). pp. 1-10.

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Abstract

In this short note, we give an elementary proof of the following well-known theorem. Let X and Y be compact Hausdorff spaces. If ρ: C(X) → C(Y) is a unital homomorphism, then there exists a continuous function p: Y → X such that (ρ(f))(y) = f(p(y)), x ∈ X, y ∈ Y, f ∈ C(X). © Indian Mathematical Society, 2022.

Item Type:	Journal Article
Publication:	Mathematics Student
Publisher:	The Indian Mathematical Society
Additional Information:	The copyright for this article belongs to the The Indian Mathematical Society.
Keywords:	Homomorphisms; Linear functionals; Linear maps
Department/Centre:	Administration > Other Offices Others
Date Deposited:	09 Nov 2022 05:16
Last Modified:	09 Nov 2022 05:18
URI:	https://eprints.iisc.ac.in/id/eprint/77652

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