generalized rings of measurable and 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.

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...

Primeness in Near-rings of Continuous Functions

Various types of primeness have been considered for near-rings. One of these is the concept of equiprime, which was defined in 1990 by Booth, Groenewald and Veldsman. We will investigate when the near-ring N0(G) of continuous zeropreserving self maps of a topological group G is equiprime. This is the case when G is either T0 and 0-dimensional or T0 and arcwise connected. We also give conditions...

Invariant Means on Spaces of Continuous or Measurable Functions ( )

1. Introduction. Invariant means on spaces of functions have been studied by von Neumann [ 7], Banach [ 2], Day [ 4], [5] and others. Day's Amenable semigroups [5] presents a comprehensive summary of the earlier work and many new results. Let 2 be an abstract group or semigroup and ret (2) the Banach space of all bounded real-valued functions on 2 with the supremum norm. A mean on rei(2) is a p...