Totally Lindelöf and totally ω-narrow paratopological groups
Metadatos
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http://dx.doi.org/10.1016/j.topol.2007.05.017 |
Metadatos
Título
Totally Lindelöf and totally ω-narrow paratopological groupsFecha de publicación
2008-01Editor
ElsevierISSN
0166-8641Cita bibliográfica
Topology and its Applications, 155, 4, p. 322-334Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.sciencedirect.com/science/article/pii/S0166864107003185Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
In many natural objects of topological algebra that possess the algebraic structure of a group, the operations of
inversion and multiplication are not necessarily continuous—it suffices to recall the groups of ... [+]
In many natural objects of topological algebra that possess the algebraic structure of a group, the operations of
inversion and multiplication are not necessarily continuous—it suffices to recall the groups of homeomorphisms
of topological spaces with the pointwise convergence topology (where the composition of homeomorphisms as
multiplication is almost never continuous). This gave rise to the study of semitopological, quasitopological, and
paratopological groups, among other related structures.
In a paratopological group, multiplication is jointly continuous while inversion is usually not—otherwise it is a
topological group. The growing interest in the study of semitopological and paratopological groups led to a significant
clarification of the importance of “topological symmetry” (i.e., the continuity of inversion) in topological algebra.
It was shown, for example, that every pseudocompact paratopological group is a topological group [7] and every
Cˇ ech-complete semitopological group is also a topological group [5]. In [2], it was established that every σ -compact
paratopological group has countable cellularity, thus generalizing a theorem from [9] proved there for topological
groups. It is worth mentioning that every precompact paratopological group has countable cellularity as well (see [4]).
The main objects of our study are the classes of totally ω-narrow and totally Lindelöf paratopological groups. [-]
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