Nest generated intersection rings in Tychonoff spaces

Minimal Quasi-F Covers of Realcompact Spaces

“…realcompact) space. The following notion due to E. F. Steiner is the basic device in the present setting [13,14]. Definition 2.1.…”

“…called the trace of F on the subspace S of X, belongs to L(S) [13,Lemma 1.3]. For any F ∈ L(X), let (ω(X, F), w X ) be the Wallman compactification of X associated with F [12,13].…”

Round subsets of Wallman-type compactifications

“…Recently, the Wallmantype (real-) compactification <w(3T), (v(2£) respectively) has been studied. (See Alo and Shapiro (1968), Gagrat and Naimpally (1973), Njastad (1966), Steiner and Steiner (1970), Su (1975).) Mandelker (1969) studied the round z -filters and round subsets of jSX.…”

“…A normal base 3E of a space X is a base for closed subsets of X which satisfies the following conditions: (i) 3£ is a ring (i.e., closed under finite unions and intersections), (ii) 2f is [2] Wallman-type 225 disjunctive (i.e., if x is not contained in the closed subset A of X, then there is a Z E 2£ such that xEZCX-A), (iii) 2t is normal (i.e., A, B E 2£ and A n B = 0 , then there exist sets C,DE3? such that A C X -C , BcX-D and C U D = X (See , Gagrat and Naimpally (1973), Njastad (1966), Steiner and Steiner (1970) and Su (1975).) Let 2T be a family of closed subsets of X.…”

“…such that Z = fl{Z n : n E N}. (See , Alo, Shapiro and Weir, Steiner (1966) and Steiner and Steiner (1970).) 2£ is said to be complement generated if for each Z E 3?…”