Abstract
Let X be a locally compact space and (Y, d) be a boundedly compact metric space. We characterize compact subsets of the space Q(X, Y) of quasicontinuous functions from X to Y equipped with the topology of uniform convergence on compact sets.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baire, R.: Sur les functions des variables reelles. Ann. Mat. Pura Appl. 3, 1–122 (1899)
Beer, G.: Topologies on Closed and Closed Convex Sets. Kluwer Academic Publishers, Dordrecht (1993)
Bouziad, A.: Every Čech-analytic Baire semitopological group is a topological group. Proc. Am. Math. Soc. 124, 953–959 (1996)
Crannell, A., Frantz, M., LeMasurier, M.: Closed relations and equivalence classes of quasicontinuous functions. Real Anal. Exch. 31, 409–424 (2006/2007)
Giles, J.R., Bartlett, M.O.: Modified continuity and a generalization of Michael’s selection theorem. Set Valued Anal. 1, 247–268 (1993)
Holá, Ľ., Holý, D.: Minimal usco maps, densely continuous forms and upper semicontinuous functions. Rocky Mt. Math. J. 39, 545–562 (2009)
Holá, Ľ., Holý, D.: Pointwise convergence of quasicontinuous mappings and Baire spaces. Rocky Mt. Math. J. 41, 1883–1894 (2011)
Holá, Ľ., Holý, D.: New characterization of minimal CUSCO maps. Rocky Mt. Math. J. 44, 1851–1866 (2014)
Holá, Ľ., Holý, D.: Quasicontinuous subcontinuous functions and compactness. Mediterr. J. Math. 13, 4509–4518 (2016)
Holá, Ľ.: Functional characterization of \(p\)-spaces. Cent. Eur. J. Math. 11, 2197–2202 (2013)
Holý, D. : Ascoli-type theorems for locally bounded quasicontinuous functions, minimal usco and minimal cusco maps. Ann. Funct. Anal. 6(3), 29–41 (2015). http://projecteuclid.org/afa
Hammer, S.T., McCoy, R.A.: Spaces of densely continuous forms. Set Valued Anal. 5, 247–266 (1997)
Kelley, J.L.: General Topology. Van Nostrand, New York (1955)
Kempisty, S.: Sur les fonctions quasi-continues. Fundam. Math. 19, 184–197 (1932)
Kenderov, P.S., Kortezov, I.S., Moors, W.B.: Continuity of quasi-continuous mappings. Topol. Appl. 109, 321–346 (2001)
Moors, W.B.: Any semitopological group that is homeomorphic to a product of Čech-complete spaces is a topological group. Set Valued Var. Anal. 21, 627–633 (2013)
Moors, W.B.: Fragmentable mappings and CHART groups. Fundam. Math. 234, 191–200 (2016)
Moors, W.B.: Semitopological groups, Bouziad spaces and topological groups. Topol. Appl. 160, 2038–2048 (2013)
Neubrunn, T.: Quasi-continuity. Real Anal. Exch. 14, 259–306 (1988)
Vaughan, H.: On locally compact metrizable spaces. Bull. Am. Math. Soc. 43, 532–535 (1937)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was completed with the support of our
-pert.
Rights and permissions
About this article
Cite this article
Holá, Ľ., Holý, D. Quasicontinuous Functions and Compactness. Mediterr. J. Math. 14, 219 (2017). https://doi.org/10.1007/s00009-017-1014-7
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-017-1014-7