Rings of Uniformly Continuous Functions
نویسندگان
چکیده
There is a natural bijective correspondence between the compactifications of a Tychonoff space X, the totally bounded uniformities on X, and the unital C∗-subalgebras of C∗(X) (the algebra of bounded continuous complex valued functions on X) with what we call the completely regular separation property. The correspondence of compactifications with totally bounded uniformities is well know and can be found in several books on general topology (e.g. [3]). The correspondence with C∗-subalgebras of C∗(X) is more obscure, and we have not found it explicitly stated in the literature. We offer a new proof of this three way correspondence.
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