Wallman spaces and compactifications

Wallman compactifications onE-completely regular spaces

“…They also gave an example of a space which is an η(X 9 JF) but not realcompact. E F. Steiner [12] generalized Frink's results and established the necessary and sufficient conditions for a Wallman space to be a compactification. The Steiners [13] used the notion of separating (see Definition 3) nest generated intersection rings (see (1.1), [13]) and studied the Wallman compactification Ύ/^(X, ά?")…”

“…Recently, the relations between Stone-Cech compactiίications and Wallman compactifications, and those between realcompactiίications and Wallman compactifications have been studied by Frink [7], Njastad [11], the Steiners [12], [13], Alo and Shapiro [1], [2], [3], [4], and some others.…”

A generalized topological measure theory

“…There has been a considerable effort in recent years to solve Frink's conjecture; and, as a result, many types of compactifications are known to be Wallman. (For instance, the reader is referred to [5], [14], [18].) If Frink's conjecture is true, then by Theorem 3.12 the problem has a positive answer.…”

The Stone-Čech compactification, the Stone-Čech remainder, and the regular Wallman property

“…A compact space is regular Wallman if it has a normal base consisting of regular closed sets. Every regular Wallman space is a Wallman compactification of each of its dense subspaces [10].…”