Uniform box products. II (Q2800382)

The uniform box topology is defined on the product set of infinitely many copies of a completely regular space, and it is finer than the Tychonoff topology but coarser than the box topology.NEWLINENEWLINEIf the space is compact, then there exists a unique uniformity which generates the topology. Otherwise, there may exist many uniformities. Even, if two uniformities generate the same topology their respective uniform box products may differ.NEWLINENEWLINETo remedy this situation the authors focus on uniformities introduced by a compactification and which are totally bounded. Hence, if restricting the property the uniform box product of a connected uniform space is connected again.NEWLINENEWLINEFurther, the authors show that the countable uniform box product of a \(\sigma\)-compact, locally compact countable-closure space is pseudonormal.NEWLINENEWLINEAt last it is proved that the countable uniform box product of any ordinal space is pseudonormal.NEWLINENEWLINE For part I see [the first author, Proc. Am. Math. Soc. 142, No. 6, 2161--2171 (2014; Zbl 1294.54011)].