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

Mandeep Kumar; Brij Kishore Tyagi

doi:10.4995/agt.2022.16925

Authors

Mandeep Kumar University of Delhi https://orcid.org/0000-0001-8773-0927
Brij Kishore Tyagi University of Delhi https://orcid.org/0000-0003-2660-2432

DOI:

https://doi.org/10.4995/agt.2022.16925

Keywords:

Quasicontinuous functions, Topology of pointwise convergence, Character, Density, Weight, Cellularity, Spread, Induced map, Restriction map

Abstract

For topological spaces X and Y, let Q_p(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 Q_p(X,Y). We also discuss the properties of the restriction and induced maps related to the space Q_p(X,Y).

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Author Biographies

Mandeep Kumar, University of Delhi

Department of Mathematics

Brij Kishore Tyagi, University of Delhi

Department of Mathematics, Atmaram Sanatan Dharma College

References

A. V. Arhangel'skii, Topological Function Spaces, Mathematics and its Applications (Soviet Series), vol. 78, Kluwer Academic Publishers Group, Dordrecht, 1992.

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), 409-424. https://doi.org/10.14321/realanalexch.31.2.0409

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), 545-562. https://doi.org/10.1216/RMJ-2009-39-2-545

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. https://doi.org/10.2478/s12175-010-0029-3

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, Berlin, 1988. https://doi.org/10.1007/BFb0098389

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