Geodesic
On a theorem of W.W. Comfort and K.A. Ross
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 133-151

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A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is $C$-embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group $G$ and prove that every $G_\delta $-dense subspace $Y$ of a topological group $G$, such that the canonical uniform tightness of $G$ is countable, is $C$-embedded in $G$.
A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is $C$-embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group $G$ and prove that every $G_\delta $-dense subspace $Y$ of a topological group $G$, such that the canonical uniform tightness of $G$ is countable, is $C$-embedded in $G$.
Classification : 22A05, 54A05, 54C45, 54D55, 54D60, 54H11
Keywords: topological group; pseudocompact; Frechet-Urysohn; $G_\delta $-dense; $C$-embed\-ded; Moscow space; canonical uniform tightness; Hewitt completion; Rajkov completion; bounded set; extremally disconnected; normal space; $k_1$-space 
Arhangel'skii, A. V. On a theorem of W.W. Comfort and K.A. Ross. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 133-151. http://geodesic.mathdoc.fr/item/CMUC_1999_40_1_a9/
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     title = {On a theorem of {W.W.} {Comfort} and {K.A.} {Ross}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {133--151},
     year = {1999},
     volume = {40},
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     zbl = {1060.54513},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_1_a9/}
}
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