Mostrar el registro sencillo del ítem
Feebly compact paratopological groups and real-valued functions
dc.contributor.author | Sanchis López, Manuel | |
dc.contributor.author | Tkachenko, Mikhail | |
dc.date.accessioned | 2013-06-18T09:59:56Z | |
dc.date.available | 2013-06-18T09:59:56Z | |
dc.date.issued | 2012 | |
dc.identifier.issn | 1436-5081 | |
dc.identifier.issn | 0026-9255 | |
dc.identifier.uri | http://hdl.handle.net/10234/67300 | |
dc.description.abstract | We present several examples of feebly compact Hausdorff paratopological groups (i.e., groups with continuous multiplication) which provide answers to a number of questions posed in the literature. It turns out that a 2-pseudocompact, feebly compact Hausdorff paratopological group G can fail to be a topological group. Our group G has the Baire property, is Fréchet–Urysohn, but it is not precompact. It is well known that every infinite pseudocompact topological group contains a countable non-closed subset. We construct an infinite feebly compact Hausdorff paratopological group G all countable subsets of which are closed. Another peculiarity of the group G is that it contains a nonempty open subsemigroup C such that C−1 is closed and discrete, i.e., the inversion in G is extremely discontinuous. We also prove that for every continuous real-valued function g on a feebly compact paratopological group G , one can find a continuous homomorphism φ of G onto a second countable Hausdorff topological group H and a continuous real-valued function h on H such that g=h∘φ . In particular, every feebly compact paratopological group is R3 -factorizable. This generalizes a theorem of Comfort and Ross established in 1966 for real-valued functions on pseudocompact topological groups. | ca_CA |
dc.format.extent | 16 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Springer-Verlag | ca_CA |
dc.relation.isPartOf | Monatshefte für Mathematik (2012) 168, 3-4 | ca_CA |
dc.rights | © Springer-Verlag | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | Paratopological group | ca_CA |
dc.subject | Feebly compact | ca_CA |
dc.subject | 2-Pseudocompact | ca_CA |
dc.subject | Precompact | ca_CA |
dc.subject | Regularization | ca_CA |
dc.subject | R3 -factorizable | ca_CA |
dc.title | Feebly compact paratopological groups and real-valued functions | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | http://dx.doi.org/10.1007/s00605-012-0444-3 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | http://link.springer.com/content/pdf/10.1007%2Fs00605-012-0444-3.pdf | ca_CA |
dc.type.version | info:eu-repo/semantics/sumittedVersion |
Ficheros en el ítem
Este ítem aparece en la(s) siguiente(s) colección(ones)
-
MAT_Articles [764]
Articles de publicacions periòdiques