The locally fine coreflection and normal covers in the products of partition-complete spaces

Abstract

We prove that the countable product of supercomplete spaces having a countable closed cover consisting of partition-complete subspaces is supercomplete with respect to its metric-fine coreflection. Thus, countable products of σ-partition-complete paracompact spaces are again paracompact. On the other hand, we show (Theorem 7.5) that in arbitrary products of partition-complete paracompact spaces, all normal covers can be obtained via the locally fine coreflection of the product of fine uniformities. These results extend those given in [1], [6], [7], [19], [30], [20], [33].

Monocoreflections of Completely Regular Frames

“…Pelant [25] gives a more direct description ofν and the later articles [14] and [15] make extensive use of this. Pelant's description allows transfinite induction arguments to check for membership inν.…”