Cardinal invariants and special maps of quasicontinuous functions with the topology of pointwise convergence

• Kumar, Mandeep ^[1] ; Tyagi, Brij Kishore ^[1]
  1. [1] University of Delhi

     University of Delhi

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 2, 2022, págs. 303-314
• Idioma: inglés
• DOI: 10.4995/agt.2022.16925
• Enlaces
  • Texto completo
• Resumen

  • For topological spaces X and Y, let Qp(X,Y) be the space of all quasicontinuous functions from X to Y with the topology of pointwise convergence. In this paper, we study the cardinal invariants such as cellularity, character, weight, density, pseudocharacter and spread of the space Qp(X,Y). We also discuss the properties of the restriction and induced maps related to the space Qp(X,Y).

• Referencias bibliográficas
  • A. V. Arhangel'skii, Topological Function Spaces, Mathematics and its Applications (Soviet Series), vol. 78, Kluwer Academic Publishers...
  • J. Borsík, Points of continuity, quasicontinuity and cliquishness, Rend. Istit. Mat. Univ. Trieste 26 (1994), 5-20.
  • R. Cazacu and J. D. Lawson, Quasicontinuous functions, domains, and extended calculus, Appl. Gen. Topol. 8 (2007), 1-33. https://doi.org/10.4995/agt.2007.1908
  • A. Crannell, M. Frantz and M. LeMasurier, Closed relations and equivalence classes of quasicontinuous functions, Real Anal. Exchange 31 (2005/06),...
  • R. Engelking, General Topology, Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989.
  • L. Holá and D. Holý, Minimal {USCO} maps, densely continuous forms and upper semi-continuous functions, Rocky Mountain J. Math. 39 (2009),...
  • L. Holá and D. Holý, Pointwise convergence of quasicontinuous mappings and {B}aire spaces, Rocky Mountain J. Math. 41 (2011), 1883-1894. https://doi.org/10.1216/RMJ-2011-41-6-1883
  • L. Holá and D. Holý, Quasicontinuous functions and the topology of pointwise convergence, Topology Appl. 282 (2020), Article No. 107301. https://doi.org/10.1016/j.topol.2020.107301
  • D. Holý and L. Matejíčka, Quasicontinuous functions, minimal {USCO} maps and topology of pointwise convergence, Math. Slovaca 60 (2010), 507-520....
  • S. Kempisty, Sur les fonctions quasicontinues, Fundamenta Mathematicae 19 (1932), 184-197. https://doi.org/10.4064/fm-19-1-184-197
  • P. S. Kenderov, I. S. Kortezov and W. B. Moors, Topological games and topological groups, Topology Appl. 109 (2001), 157-165. https://doi.org/10.1016/S0166-8641(99)00152-2
  • P. S. Kenderov, I. S. Kortezov and W. B. Moors, Continuity points of quasi-continuous mappings, Topology Appl. 109 (2001), 321-346. https://doi.org/10.1016/S0166-8641(99)00180-7
  • 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
  • R. A. McCoy and I. Ntantu, Topological Properties of Spaces of Continuous Functions, Lecture Notes in Mathematics, vol. 1315, Springer-Verlag,...
  • T. Neubrunn, Quasi-continuity, Real Anal. Exchange 14 (1988/89), 259-306. https://doi.org/10.2307/44151947
  • Z. Piotrowski, A survey of results concerning generalized continuity of topological spaces, Acta Math. Univ. Comenian. 52/53 (1987), 91-110.
  • V. V. Tkachuk, A $C_p$-Theory Problem Book, Topological and function spaces, Problem Books in Mathematics, Springer, New York, 2011. https://doi.org/10.1007/978-1-4419-7442-6