Abstract
A space X is called Moscow if the closure of any open set is the union of some family of G δ-subsets of X. It is established that if a topological ring K of non-measurable cardinality is a Moscow space, then the operations in K can be continuously extended to the Hewitt–Nachbin completion υK of K turning υK into a topological ring as well. A similar fact is established for linear topological spaces. If F is a topological field such that the cardinality of F is non-measurable and the space F is Moscow, then the space F is submetrizable and the space F is hereditarily Hewitt–Nachbin complete. In particular, υF=F. We also show the effect of homogeneity of the Hewitt–Nachbin completion on the commutativity of the Hewitt–Nachbin completion with the product operation.
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Arhangel'skii, A.V. The Hewitt–Nachbin Completion in Topological Algebra. Some Effects of Homogeneity. Applied Categorical Structures 10, 267–278 (2002). https://doi.org/10.1023/A:1015234708772
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DOI: https://doi.org/10.1023/A:1015234708772