Local compactness and Hewitt realcompactifications of products II

Dieudonné Completion and PT-Groups

“…It is well known that every feathered group is a paracompact M-space [15] and that every paracompact M-space is of pointwise countable type. It was established in [14,Theorem 24.1] that the formula μ(X × Y) = μX × Y holds for every weak cb * -space X and a paracompact M-space Y. However, the argument given in [14] implies the following more general fact: Proposition 4.5 If X is a weak cb * -space and Y is a paracompact space of pointwise countable type, then μ(X × Y) = μX × Y.…”

“…We recall that X is said to be a weak cb * -space if for every decreasing sequence F 0 ⊇ F 1 ⊇ · · · ⊇ F n ⊇ · · · of regular closed sets in X with empty intersection, the intersection of their closures in υ X is also empty [12,14]. The next simple but helpful fact is Theorem 17.2 (g) from [14]:…”

“…In particular, μM = M, and the groups G and M are completion friendly. We now apply [14,Theorem 19.2] which states that if X is a weak cb * -space with υ X = μX and Y is a paracompact space of pointwise countable type, then…”