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- W3015688999 abstract "For a Tychonoff space X, the Dieudonné τ-completion of X, denoted by μτX, is investigated. The space μτX is defined as the completion of X with respect to the uniformity uXτ, where uXτ is generated by all continuous mappings of X to metric spaces of weight ≤τ. It is proved that a dense subspace Y of X is Pτ-(equivalently, Pτ⁎-)embedded in X iff uXτ|Y=uYτ iff Y⊂X⊂μτX. In this case, the free topological group F(uYτY) of the uniform space uYτY is the topological subgroup of the group F(uXτX) generated by Y iff Y is Pτ-embedded in X. This result implies the Nummela-Pestov's Theorem: A dense subspace Y is P-embedded in a Tychonoff space X iff the free topological group F(Y) is topologically isomorphic to the subgroup of the group F(X) generated by Y. It is proved that the Weil completion of the free topological group coincides with its Raĭkov completion. It is also shown that the free topological groups in the sense of Nakayama and Nummela coincide." @default.
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- W3015688999 date "2020-08-01" @default.
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- W3015688999 title "The Dieudonné τ-complete spaces and free topological groups of uniform spaces" @default.
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- W3015688999 doi "https://doi.org/10.1016/j.topol.2020.107210" @default.
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