PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 2 | 1 |
Tytuł artykułu

A note on pseudobounded paratopological groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group. We present some examples of paratopological groups with interesting properties: (1) There exists a metrizable, zero-dimensional and pseudobounded topological group; (2) There exists a Hausdorff ω-pseudobounded paratopological group G such that G contains a dense subgroup which is not ω-pseudobounded; (3) There exists a Hausdorff connected paratopological group which is not ω-pseudobounded.
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2013-11-30
zaakceptowano
2014-02-01
online
2014-06-27
Twórcy
autor
  • School of mathematics and statistics, Minnan Normal University, Zhangzhou 363000, P. R. China, linfu-cai2008@aliyun.com
autor
  • Institute of Mathematics, Ningde Teachers’ College, Ningde, Fujian 352100, P. R. China, shoulin60@163.com
  • Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael
    Atlixco 186, Col. Vicentina, Del. Iztapalapa, C.P. 09340, Mexico, D.F., isr.uami@gmail.com
Bibliografia
  • [1] O.T. Alas, M. Sanchis, Countably compact paratopological groups, Semigroup Forum 74 (2007) 423–438.[WoS]
  • [2] A.V. Arhangel’skii, E.A. Reznichenko, Paratopological and semitopological groups versus topological groups, TopologyAppl. 151 (2005) 107–119.
  • [3] A.V. Arhangel’skii, M.G. Tkachenko, Topological groups and related structures, Atlantis Studies in Mathematics, Vol. I,Atlantis Press/World Scientific, Paris-Amsterdam, 2008.
  • [4] K. H. Azar, Bounded topological groups, arXiv: 1003.2876.
  • [5] T. Banakh, I. Guran, O. Ravsky, Characterizing meager paratopological groups, Applied General Topology, 12(1)(2011) 27–33.
  • [6] R. Engelkig, General Topology, Heldermann Verlag, Berlin, 1989.
  • [7] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis. Vol. I, Structure of Topological Groups, Integration Theory, GroupRepresentations. Second edition. Fund. Prin. of Math. Sci., 115. (Springer-Verlag, Berlin-New York, 1979).
  • [8] F. Lin and S. Lin, Pseudobounded or !-pseudobounded paratopological groups, Filomat, 25:3 (2011) 93–103.[WoS]
  • [9] F. Lin and C. Liu, On paratopological groups, Topology Apply., 159 (2012) 2764–2773.[WoS]
  • [10] O.V. Ravsky, Paratopological groups I, Matematychni Studii 16 (2001), No. 1, 37–48.[WoS]
  • [11] O.V. Ravsky, Paratopological groups II, Matematychni Studii 17 (2002), No. 1, 93–101.[WoS]
  • [12] O.V. Ravsky, Pseudocompact paratopological groups that are topological, http://arxiv.org/abs/1003.5343 (April 7, 2012).
  • [13] M. Sanchis, M.G. Tkachenko, Totally Lindelöf and totally !-narrow paratopological groups, Topology Apply. 155 (2007)322–334.
  • [14] M. Tkachenko, Group reflection and precompact paratopological groups, Topological Algebra and its Applications,(2013) 22–30.
  • [15] M. Tkachenko, Embedding paratopological groups into topological products, Topol. Appl., 156(2009) 1298-1305.[WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_taa-2014-0003
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.