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Axioms 2015, 4(3), 254-267; doi:10.3390/axioms4030254

Lindelöf Σ-Spaces and R-Factorizable Paratopological Groups

Universidad Autónoma Metropolitana, Iztapalapa Campus, Av. San Rafael Atlixco 187, Col. Vicentina, C.P. 09340 Iztapalapa, Mexico City, Mexico
Academic Editor: Sidney A. Morris
Received: 17 April 2015 / Revised: 25 June 2015 / Accepted: 30 June 2015 / Published: 10 July 2015
(This article belongs to the Special Issue Topological Groups: Yesterday, Today, Tomorrow)
View Full-Text   |   Download PDF [235 KB, uploaded 10 July 2015]

Abstract

We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally w-narrow and satisfies celw(G) ≤ w, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group. View Full-Text
Keywords: cellularity; network; Gδ-diagonal; R-factorizable; w-cellular; w-narrow; totally w-narrow cellularity; network; Gδ-diagonal; R-factorizable; w-cellular; w-narrow; totally w-narrow
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Tkachenko, M. Lindelöf Σ-Spaces and R-Factorizable Paratopological Groups. Axioms 2015, 4, 254-267.

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