Let C(f), Q(f), E(f) and A(f) be the sets of all continuity, quasicontinuity, upper and lower quasicontinuity and cliquishness points of a real function f: X → ℝ, respectively. The triplets (C(f),Q(f),A(f)), (C(f),E(f),A(f) and (Q(f),E(f),A(f)are characterized for functions defined on Baire metric spaces without isolated points.
@article{bwmeta1.element.doi-10_2478_s11533-009-0071-y,
author = {J\'an Bors\'\i k},
title = {Points of continuity and quasicontinuity},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {179-190},
zbl = {1204.54010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0071-y}
}
Ján Borsík. Points of continuity and quasicontinuity. Open Mathematics, Tome 8 (2010) pp. 179-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0071-y/
[1] Borsík J., On the points of bilateral quasicontinuity of functions, Real Anal. Exchange, 1993/94, 19, 529–536 | Zbl 0807.26002
[2] Borsík J., Points of continuity, quasicontinuity, cliquishness and upper and lower quasicontinuity, Real Anal. Exchange, 2007/2008, 33, 339–350 | Zbl 1162.54003
[3] Borsík J., Sums of quasicontinuous functions defined on pseudometrizable spaces, Real Anal. Exchange, 1996/97, 22, 328–337 | Zbl 0879.54014
[4] Ewert J., Lipski T., Lower and upper quasicontinuous functions, Demonstratio Math., 1983, 16, 85–93 | Zbl 0526.54005
[5] Lipinski J.S., Šalát T., On the points of quasicontinuity and cliquishness of functions, Czechoslovak Math. J., 1971, 21, 484–489 | Zbl 0219.26004
[6] Neubrunn T., Quasi-continuity, Real Anal. Exchange, 1988/89, 14, 259–306
[7] Neubrunnová A., On quasicontinuous and cliquishfunctions, Časopis Pěst. Mat., 1974, 99, 109–114 | Zbl 0292.26005
[8] Stronska E., Maximal families for the class of upper and lower semi-quasicontinuous functions, Real Anal. Exchange, 2001/2002, 27, 599–608 | Zbl 1068.26009