Let X be a completely regular space, and let A(X) be a subalgebra of C(X) containing C*{X). We study the maximal ideals in A(X) by associating a filter Z(f) to each / 6 A(X). This association extends… (More)

The theory of topological algebras and the theory of bases in topological vector spaces are both well-established areas of analysis but only recently have papers appeared combining these two… (More)

Let X be a completely regular topological space. An intermediate ring is a ring A(X) of continuous functions satisfying C∗(X) ⊆ A(X) ⊆ C(X). In Redlin andWatson (1987) and in Panman et al. (2012),… (More)

Let X be a completely regular topological space. Let A(X) be a ring of continuous functions between C∗(X) and C(X), that is C∗(X) ⊆ A(X) ⊆ C(X). In [9], a correspondence ZA between ideals of A(X) and… (More)

In most real analysis textbooks, the standard example of a nonmeasurable set is a subset of the real line that is due to Vitali [3]. We describe a similar nonmeasurable subset of the torus (and hence… (More)

Let X , Y , and Z be random variables. If X is positively correlated to Y and Y is positively correlated to Z, it does not necessarily follow that X is positively correlated to Z. In this article we… (More)