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Order theoretic variants of the fundamental theorem of compact semigroups.

S.D. Hippisley-Cox (1994)

Semigroup forum

Ordinals in topological groups

Raushan Z. Buzyakova (2007)

Fundamenta Mathematicae

We show that if an uncountable regular cardinal τ and τ + 1 embed in a topological group G as closed subspaces then G is not normal. We also prove that an uncountable regular cardinal cannot be embedded in a torsion free Abelian group that is hereditarily normal. These results are corollaries to our main results about ordinals in topological groups. To state the main results, let τ be an uncountable regular cardinal and G a T₁ topological group. We prove, among others, the following statements:...

$P D$ -( $C$ -) пары расширений минимальных полугрупп преобразований

А.И. Герко (1990)

Matematiceskie issledovanija

Paracompact Topological Groups and Uniform Continuity

Ofelia T. Alas (1973)

Monatshefte für Mathematik

Perfect mappings in topological groups, cross-complementary subsets and quotients

Aleksander V. Arhangel'skii (2003)

Commentationes Mathematicae Universitatis Carolinae

The following general question is considered. Suppose that $G$ is a topological group, and $F$ , $M$ are subspaces of $G$ such that $G = M F$ . Under these general assumptions, how are the properties of $F$ and $M$ related to the properties of $G$ ? For example, it is observed that if $M$ is closed metrizable and $F$ is compact, then $G$ is a paracompact $p$ -space. Furthermore, if $M$ is closed and first countable, $F$ is a first countable compactum, and $F M = G$ , then $G$ is also metrizable. Several other results of this kind are obtained....

Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology

Taras Banakh, Igor Guran (2013)

Topological Algebra and its Applications

In this paper we introduce perfectly supportable semigroups and prove that they are σ-discrete in each Hausdorff shiftinvariant topology. The class of perfectly supportable semigroups includes each semigroup S such that FSym(X) ⊂ S ⊂ FRel(X) where FRel(X) is the semigroup of finitely supported relations on an infinite set X and FSym(X) is the group of finitely supported permutations of X.