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Selections and suborderability

Giuliano Artico, Umberto Marconi, Jan Pelant, Luca Rotter, Mikhail Tkachenko (2002)

Fundamenta Mathematicae

We extend van Mill-Wattel's results and show that each countably compact completely regular space with a continuous selection on couples is suborderable. The result extends also to pseudocompact spaces if they are either scattered, first countable, or connected. An infinite pseudocompact topological group with such a continuous selection is homeomorphic to the Cantor set. A zero-selection is a selection on the hyperspace of closed sets which chooses always an isolated point of a set. Extending Fujii-Nogura...

Semi-quotient mappings and spaces

Moiz ud Din Khan, Rafaqat Noreen, Muhammad Siddique Bosan (2016)

Open Mathematics

In this paper, we continue the study of s-topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups (G, *, τ) the semi-quotient space G/H is regular. Semi-isomorphisms of s-topological groups are also discussed.

Semitopological homomorphisms

Anna Giordano Bruno (2008)

Rendiconti del Seminario Matematico della Università di Padova

Sequential continuity on dyadic compacta and topological groups

Aleksander V. Arhangel'skii, Winfried Just, Grzegorz Plebanek (1996)

Commentationes Mathematicae Universitatis Carolinae

We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.

Sequential convergences in $ℓ$ -groups without Urysohn’s axiom

Ján Jakubík (1992)

Czechoslovak Mathematical Journal

Sequential convergences on free lattice ordered groups

Ján Jakubík (1992)

Mathematica Bohemica

In this paper the partially ordered set Conv $G$ of all sequential convergences on $G$ is investigated, where $G$ is either a free lattice ordered group or a free abelian lattice ordered group.

Sequential topological groups of any sequential order under CH

Alexander Shibakov (1998)

Fundamenta Mathematicae

For any $α < ω_{1}$ a countable sequential topological group of sequential order α is constructed using CH.

Some large and small sets in topological groups.

Artico, Giuliano, Malykhin, Viatcheslav I., Marconi, Umberto (2001)

Mathematica Pannonica

Some questions of Arhangel'skii on rotoids

Harold Bennett, Dennis Burke, David Lutzer (2012)

Fundamenta Mathematicae

A rotoid is a space X with a special point e ∈ X and a homeomorphism F: X² → X² having F(x,x) = (x,e) and F(e,x) = (e,x) for every x ∈ X. If any point of X can be used as the point e, then X is called a strong rotoid. We study some general properties of rotoids and prove that the Sorgenfrey line is a strong rotoid, thereby answering several questions posed by A. V. Arhangel'skii, and we pose further questions.

Some results on compact convergence semigroups defined by filters.

Ho, Phoebe, Plummer, Paul, So, Shing (1998)

International Journal of Mathematics and Mathematical Sciences

Splitting in locally compact abelian groups

Peter Loth (1998)

Rendiconti del Seminario Matematico della Università di Padova

Strict completions of $ℒ_{0}^{*}$ -groups

Roman Frič, Fabio Zanolin (1992)

Czechoslovak Mathematical Journal

Subgroups and products of $ℝ$ -factorizable $P$ -groups

Constancio Hernández, Mihail G. Tkachenko (2004)

Commentationes Mathematicae Universitatis Carolinae

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

Subgroups of $ℝ$ -factorizable groups.

Hernández, Constancio, Tkačenko, Michael (1998)

Commentationes Mathematicae Universitatis Carolinae

Subgroups of $ℝ$ -factorizable groups

Constancio Hernández, Mihail G. Tkachenko (1998)

Commentationes Mathematicae Universitatis Carolinae

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

Summable Family in a Commutative Group

Roland Coghetto (2015)

Formalized Mathematics

Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6]. First, we compare the notions of the limit of a family indexed by a directed set, or a sequence, in a metric space [30], a real normed linear space [29] and a linear topological space [14] with the concept of the limit of an image filter [16]. Then, following Bourbaki [9], [10] (TG.III, §5.1 Familles sommables...

Sur une version algébrique de la notion de sous-groupe minimal relatif de $ℝ^{n}$

Damien Roy (1990)

Bulletin de la Société Mathématique de France

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