Free paratopological groups

• Autores: Ali Sayed Elfard
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 2, 2015, págs. 89-98
• Idioma: inglés
• DOI: 10.4995/agt.2015.1874
• Enlaces
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• Resumen

  • Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove that the group FP(X) is an Alexandroff space if X is an Alexandroff space. Moreover, we introduce a~neighborhood base at the identity of the group FP(X) when the space X is Alexandroff and then we give some properties of this neighborhood base. As applications of these, we prove that the group FP(X) is T_0 if X is T_0, we characterize the spaces X for which the group FP(X) is a topological group and then we give a class of spaces $X$ for which the group FP(X) has the inductive limit property.

• Referencias bibliográficas
  • F. G. Arenas, Alexandroff spaces, Acta Math. Univ. Comenian. (N.S.) 68 (1999), 17-25.
  • A.V. Arhangel'skii and M. G. Tkachenko, Topological groups and related structures, Atlantis Studies in Mathematics, vol.1, Atlantis Press,...
  • (http://dx.doi.org/10.2991/978-94-91216-35-0)
  • A. S. Elfard and P. Nickolas, On the topology of free paratopological groups, Bulletin of the London Mathematical Society 44, no. 6 (2012),...
  • (http://dx.doi.org/10.1112/blms/bds031)
  • A. S. Elfard and P. Nickolas, On the topology of free paratopological groups. II, Topology Appl. 160, no. 1 (2013), 220-229.
  • (http://dx.doi.org/10.1016/j.topol.2012.10.011)
  • A. S. Elfard, Free paratopological groups, PhD Thesis, University of Wollongong, Australia (2012).
  • J. Marín and S. Romaguera, A bitopological view of quasi-topological groups, Indian J. Pure Appl. Math. 27 (1996),393-405.
  • N. M. Pyrch and O.V. Ravsky, On free paratopological groups, Mat. Stud. 25 (2006), 115-125.
  • N. M. Pyrch, On isomorphisms of the free paratopological groups and free homogeneous spaces I, Visnyk Liviv Univ. Ser. Mech-Math. 63 (2005),...
  • N. M. Pyrch, On isomorphisms of the free paratopological groups and free homogeneous spaces II, Visnyk Liviv Univ. 71 (2009), 191-203.
  • P. Alexandroff, Diskrete Räume, Mat. Sb. (N.S.) 2 (1937), 501-518.
  • S. Romaguera, M. Sanchis and M. Tkacenko, Free paratopological groups, Proceedings of the 17th Summer Conference on Topology and its Applications...