Selection principles: s-Menger and s-Rothberger-bounded groups

• Iqbal, Muhammad Asad ^[1] ; Khan, Moiz ud Din ^[1]
  1. [1] COMSATS University Islamabad
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 1, 2022, págs. 189-199
• Idioma: inglés
• DOI: 10.4995/agt.2022.14846
• Enlaces
  • Texto completo
• Resumen

  • In this paper, selection principles are defined and studied in the realm of irresolute topological groups. Especially, s-Menger-bounded and s-Rothberger-bounded type covering properties are introduced and studied.

• Referencias bibliográficas
  • A. Arhangelskii and M. Tkachenko, Topological groups and related structures, Atlantis Studies in Mathematics, Atlantis Press, 2008.
  • https://doi.org/10.2991/978-94-91216-35-0
  • K.H. Azar, Bounded topological groups, arXiv:1003.2876.
  • L. Babinkostova, Metrizable groups and strict o-boundedness, Mat. Vesnik. 58 (2006), 131-138.
  • L. Babinkostova, Lj. DR. Kocinac and M. Scheepers, Combinatorics of open covers (VIII), Topology Appl. 140 (2004), 15-32.
  • https://doi.org/10.1016/j.topol.2003.08.019
  • T. Banakh and S. Ravsky, On subgroups of saturated or totally bounded paratopological groups, Algebra Discrete Math. 4 (2003), 1-20.
  • S. G. Crossley and S. K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), 233-254.
  • https://doi.org/10.4064/fm-74-3-233-254
  • R. Engelking, General Topology, Heldermann-Verlag, Berlin, 1989.
  • I. I. Guran, On topological groups close to being Lindelöf, Dokl. Akad. Nauk. 256 (1981), 1305-1307.
  • C. Hernández, Topological groups close to being $sigma $-compact, Topology Appl. 102 (2000), 101-111.
  • https://doi.org/10.1016/S0166-8641(98)00129-1
  • C. Hernández, D. Robbie and M. Tkachenko, Some properties of o-bounded groups and strictly o-bounded groups, Appl. Gen. Topol. 1 (2000), 29-43.
  • https://doi.org/10.4995/agt.2000.3022
  • W. Hurewicz, Uber die verallgemeinerung des borelschen theorems, Math. Z. 24 (1925), 401-425.
  • https://doi.org/10.1007/BF01216792
  • D.S. Jankovic, On locally irreducible spaces, Ann. Soc. Sci. Bruxelles. 2 (1983), 59-72.
  • M. Khan, A. Siab and Lj.DR. Kocinac, Irresolute-topological groups, Math. Morav. 19 (2015), 73-80.
  • https://doi.org/10.5937/MatMor1501073K
  • D. Kocev, Almost Menger and related spaces, Mat. Vesnik. 61 (2009), 172-180.
  • Lj. DR. Kocinac, On Menger, Rothberger and Hurewicz topological groups, Unpublished note (1998).
  • Lj. DR. Kocinac, Selected results on selection principles, Proc. Third Seminar Geo. Topo. (2004), 71-104 .
  • Lj. DR. Kocinac, Star selection principles: A survey, Khayyam J. Math. 1 (2015), 82-106.
  • Lj. DR. Kocinac, A. Sabah, M. Khan and D. Seba, Semi-Hurewicz spaces, Hacet. J. Math. Stat. 46 (2017), 53-66.
  • https://doi.org/10.15672/HJMS.2016.405
  • J. P. Lee, On semi-homeomorphisms, Internat. J. Math. 13 (1990), 129-134.
  • https://doi.org/10.1155/S0161171290000163
  • N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly. 70 (1963), 36-41.
  • https://doi.org/10.1080/00029890.1963.11990039
  • F. Lin and S. Lin, A note on pseudobounded paratopological groups, Topological Algebra Appl. 2 (2014), 11-18.
  • https://doi.org/10.2478/taa-2014-0003
  • K. Menger, Einige Uberdeckungssatze der Punktmengenlehre, Sitzungsberichte. Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik...
  • T. Noiri and B. Ahmad, Semi-contiuous mappings functions, Accad. Nazionale Dei Lincei. 10 (1982).
  • R. Noreen and M. Khan, Quasi-boundedness of irresolute paratopological groups, Cogent Math. & Stat. 5 (2018), 1-8.
  • https://doi.org/10.1080/25742558.2018.1458553
  • V. Pipitone and G. Russo, Spazi semi connessi e spazi semiaperti, Rend. Circ. Mat. Palermo. 2 (1975), 273-287.
  • https://doi.org/10.1007/BF02843735
  • A. Sabah, M. Khan and Lj. DR. Kocinac, Covering properties defined by semi-open sets, J. Nonlinear Sci. Appl. 9, 4388-4398.
  • https://doi.org/10.22436/jnsa.009.06.79
  • M. Sakai and M. Scheepers, The combinatorics of open covers, Recent Progress in General Topology III. (2014), 751-800.
  • https://doi.org/10.2991/978-94-6239-024-9_18
  • M. Scheepers, Combinatorics of open covers I: Ramsey theory, Topology Appl. 69 (1996), 31-62.
  • https://doi.org/10.1016/0166-8641(95)00067-4
  • M. Scheepers, Selection principles and covering properties in Topology, Note Mat. 2 (2003), 3-41.
  • B. Tsaban, Some new directions in infinite-combinatorial topology, Trends Math. (2006), 225-255.
  • https://doi.org/10.1007/3-7643-7692-9_7