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Sub-rings of C(Rⁿ) Gan, Cheong Kuoon

Abstract

The content of this thesis contains a study of the rings C(Rⁿ), L[sub c](Rⁿ), C[sup m](Rⁿ), C[sup ∞](Rⁿ), А(Rⁿ) and P(Rⁿ). We obtain the result that no two of the rings above can be isomorphic : in fact we prove the following : if Φ : A → B is a ring homomorphism where A, B are any two of the rings and A ⊂ B, then Φ(f) = f(p) for some p εRⁿ. We also characterise C(Rⁿ), C[sup m](Rⁿ), and C[sup ∞](Rⁿ) as rings.

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