The Locally Fine Coreflection and Normal Covers in the Products of   Partition-complete Spaces
  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 sigma-partition-complete paracompact spaces are again paracompact. On the other hand, we show 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. 
Aarno Hohti, Miroslav Husek, Jan Pelant