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It was proved in [HM] that each topological group (G,·,τ) may be embedded into a connected topological group (Ĝ,•,τ̂). In fact, two methods of introducing τ̂ were given. In this note we show relations between them.

Embedding a topological group into its WAP-compactification

Stefano Ferri, Jorge Galindo (2009)

Studia Mathematica

We prove that the topology of the additive group of the Banach space c₀ is not induced by weakly almost periodic functions or, what is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. We show, in contrast, that additive groups of Schwartz locally convex spaces are always representable as groups of isometries on some reflexive Banach space.

Embedding compact t-semigroups into compact uniquely divisible semigroups.

D.R. Brown, J.A. Hildebrant (1990)

Semigroup forum

Embedding in compact uniquely divisible semigroups.

J.D. Lawson, J.A. Hildebrant (1972)

Semigroup forum

Embedding S(X) into S(Y) [Book]

K. D. Magill, Jr., S. Subbiah (1974)

Embedding topological semigroups.

F.T. jr. Christoph (1970)

Semigroup forum

Embedding topological semigroups into the hyperspaces over topological groups

Taras O. Banakh, Olena Hryniv (2007)

Acta Universitatis Carolinae. Mathematica et Physica

Embeddings in contractible or compact objects

Ronald Brown, Sidney A. Morris (1978)

Colloquium Mathematicae

Endomorphic actions of ßN on the torus group.

W.A.F. Ruppert (1991)

Semigroup forum

Endomorphisms of the Lie algebroids $T M \times 𝔤$ up to homotopy.

Balcerzak, Bogdan, Kubarski, Jan, Walas, Witold (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Enlarging the convergence on the real line via metrizable group topologies

Yasunao Hattori (1998)

Mathematica Slovaca

Epics in the category of $T_{2}$ k-groups need not have dense range

W. F. Lamartin (1976)

Colloquium Mathematicae

Epimorphisms and semilattices of semigroups.

J. Crawley (1980)

Semigroup forum

Equicontinuous commutative semigroups of onto functions

Lawrence S. Husch (1973)

Czechoslovak Mathematical Journal

Equivalence of certain free topological groups

Jan Baars (1992)

Commentationes Mathematicae Universitatis Carolinae

In this paper we give a complete isomorphical classification of free topological groups $F M (X)$ of locally compact zero-dimensional separable metric spaces $X$ . From this classification we obtain for locally compact zero-dimensional separable metric spaces $X$ and $Y$ that the free topological groups $F M (X)$ and $F M (Y)$ are isomorphic if and only if $C_{p} (X)$ and $C_{p} (Y)$ are linearly homeomorphic.

Equivariant completions

Michael Megrelishvili (1994)

Commentationes Mathematicae Universitatis Carolinae

An important consequence of a result of Katětov and Morita states that every metrizable space is contained in a complete metrizable space of the same dimension. We give an equivariant version of this fact in the case of a locally compact $σ$ -compact acting group.

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