R-factorizable paratopological groups
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http://dx.doi.org/10.1016/j.topol.2009.08.010 |
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Title
R-factorizable paratopological groupsDate
2010Publisher
ElsevierISSN
1668641Bibliographic citation
Topology and its Applications, 157, 4, p. 800-808Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
For i = 1, 2, 3, 3.5, we define the class of R<sub>i</sub>-factorizable paratopological groups G by the condition that every continuous real-valued function on G can be factorized through a continuous homomorphism p ... [+]
For i = 1, 2, 3, 3.5, we define the class of R<sub>i</sub>-factorizable paratopological groups G by the condition that every continuous real-valued function on G can be factorized through a continuous homomorphism p : G → H onto a second countable paratopological group H satisfying the T<sub>i</sub>-separation axiom. We show that the Sorgenfrey line is a Lindelöf paratopological group that fails to be R<sub>1</sub>-factorizable. However, every Lindelöf totally ω-narrow regular (Hausdorff) paratopological group is R<sub>3</sub>-factorizable (resp. R<sub>2</sub>-factorizable). We also prove that a Lindelöf totally ω-narrow regular paratopological group is topologically isomorphic to a closed subgroup of a product of separable metrizable paratopological groups. © 2009 Elsevier B.V. All rights reserved. [-]
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