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Condensations of Tychonoff universal topological algebras

Constancio Hernández — 2001

Commentationes Mathematicae Universitatis Carolinae

Let ( L , 𝒯 ) be a Tychonoff (regular) paratopological group or algebra over a field or ring K or a topological semigroup. If nw ( L , 𝒯 ) τ and nw ( K ) τ , then there exists a Tychonoff (regular) topology 𝒯 * 𝒯 such that w ( L , 𝒯 * ) τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.

Subgroups and products of -factorizable P -groups

Constancio HernándezMihail G. Tkachenko — 2004

Commentationes Mathematicae Universitatis Carolinae

We show that subgroup of an -factorizable abelian P -group is topologically isomorphic to a subgroup of another -factorizable abelian P -group. This implies that closed subgroups of -factorizable P -groups are not necessarily -factorizable. We also prove that if a Hausdorff space Y of countable pseudocharacter is a continuous image of a product X = i I X i of P -spaces and the space X is pseudo- ω 1 -compact, then n w ( Y ) 0 . In particular, direct products of -factorizable P -groups are -factorizable and ω -stable.

The Lindelöf property and pseudo- 1 -compactness in spaces and topological groups

Constancio HernándezMihail G. Tkachenko — 2008

Commentationes Mathematicae Universitatis Carolinae

We introduce and study, following Z. Frol’ık, the class ( 𝒫 ) of regular P -spaces X such that the product X × Y is pseudo- 1 -compact, for every regular pseudo- 1 -compact P -space Y . We show that every pseudo- 1 -compact space which is locally ( 𝒫 ) is in ( 𝒫 ) and that every regular Lindelöf P -space belongs to ( 𝒫 ) . It is also proved that all pseudo- 1 -compact P -groups are in ( 𝒫 ) . The problem of characterization of subgroups of -factorizable (equivalently, pseudo- 1 -compact) P -groups is considered as well. We give some necessary...

Subgroups of -factorizable groups

Constancio HernándezMihail G. Tkachenko — 1998

Commentationes Mathematicae Universitatis Carolinae

The properties of -factorizable groups and their subgroups are studied. We show that a locally compact group G is -factorizable if and only if G is σ -compact. It is proved that a subgroup H of an -factorizable group G is -factorizable if and only if H is z -embedded in G . Therefore, a subgroup of an -factorizable group need not be -factorizable, and we present a method for constructing non- -factorizable dense subgroups of a special class of -factorizable groups. Finally, we construct a closed...

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