The Hewitt-Nachbin completion in topological algebra. Some effects of homogeneity (Q1610283)

By a previous result of the author, the Hewitt-Nachbin completion \(\upsilon{G}\) of a Moscow topological group \(G\) of non-measurable cardinality is again a topological group that contains \(G\) as a dense topological subgroup [Comment. Math. Univ. Carolin. 40, 133-151 (1999)]. In the article under review, he extends this important result to topological rings and linear topological spaces. It is also shown in the article that if a topological field \(F\) is a Moscow space of non-mesurable cardinality, then \(F\) is submetrizable (i.e., \(F\) admits a weaker metrizable topology) and, hence, the space \(F\) is hereditarily Hewitt-Nachbin complete. These results are applied to show that the Hewitt-Nachbin completion operation commutes with the product operation in several important cases.