On structure spaces of ideals in rings of continuous functions

Author:
David Rudd

Journal:
Trans. Amer. Math. Soc. **190** (1974), 393-403

MSC:
Primary 54C40; Secondary 46E25

MathSciNet review:
0350690

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Abstract: A ring of continuous functions is a ring of the form , the ring of all continuous real-valued functions on a completely regular Hausdorff space *X*.

With each ideal *I* of , we associate certain subalgebras of , and discuss their structure spaces.

We give necessary and sufficient conditions for two ideals in rings of continuous functions to have homeomorphic structure spaces.

**[1]**Leonard Gillman and Meyer Jerison,*Rings of continuous functions*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0116199****[2]**Anthony W. Hager,*On inverse-closed subalgebras of 𝐶(𝑋)*, Proc. London Math. Soc. (3)**19**(1969), 233–257. MR**0244948****[3]**J. R. Isbell,*Algebras of uniformly continuous functions*, Ann. of Math. (2)**68**(1958), 96–125. MR**0103407****[4]**David Rudd,*On isomorphisms between ideals in rings of continuous functions*, Trans. Amer. Math. Soc.**159**(1971), 335–353. MR**0283575**, 10.1090/S0002-9947-1971-0283575-1**[5]**David Rudd,*An example of a Φ-algebra whose uniform closure is a ring of continuous functions*, Fund. Math.**77**(1972), no. 1, 1–4. MR**0322788**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0350690-6

Keywords:
Rings of real-valued continuous functions,
ideals,
structure spaces,
uniform closure

Article copyright:
© Copyright 1974
American Mathematical Society