Book Review: Rings of continuous functions

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

generalized rings of measurable and continuous functions

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Concerning Rings of Continuous Functions

Rings of Uniformly Continuous Functions

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 ca...

Algebraic properties of rings of continuous functions

This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly nonnoetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness crit...