Points of continuity and quasicontinuity

Ján Borsík

Open Mathematics (2010)

  • Volume: 8, Issue: 1, page 179-190
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Ján Borsík. "Points of continuity and quasicontinuity." Open Mathematics 8.1 (2010): 179-190. <http://eudml.org/doc/269140>.

@article{JánBorsík2010,
abstract = {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.},
author = {Ján Borsík},
journal = {Open Mathematics},
keywords = {Continuity; Quasi-continuity; Cliquishness; Upper and lower quasicontinuity; continuity; quasi-continuity; cliquishness; upper and lower quasi-continuity},
language = {eng},
number = {1},
pages = {179-190},
title = {Points of continuity and quasicontinuity},
url = {http://eudml.org/doc/269140},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Ján Borsík
TI - Points of continuity and quasicontinuity
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 179
EP - 190
AB - 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.
LA - eng
KW - Continuity; Quasi-continuity; Cliquishness; Upper and lower quasicontinuity; continuity; quasi-continuity; cliquishness; upper and lower quasi-continuity
UR - http://eudml.org/doc/269140
ER -

References

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  1. [1] Borsík J., On the points of bilateral quasicontinuity of functions, Real Anal. Exchange, 1993/94, 19, 529–536 Zbl0807.26002
  2. [2] Borsík J., Points of continuity, quasicontinuity, cliquishness and upper and lower quasicontinuity, Real Anal. Exchange, 2007/2008, 33, 339–350 Zbl1162.54003
  3. [3] Borsík J., Sums of quasicontinuous functions defined on pseudometrizable spaces, Real Anal. Exchange, 1996/97, 22, 328–337 Zbl0879.54014
  4. [4] Ewert J., Lipski T., Lower and upper quasicontinuous functions, Demonstratio Math., 1983, 16, 85–93 Zbl0526.54005
  5. [5] Lipinski J.S., Šalát T., On the points of quasicontinuity and cliquishness of functions, Czechoslovak Math. J., 1971, 21, 484–489 Zbl0219.26004
  6. [6] Neubrunn T., Quasi-continuity, Real Anal. Exchange, 1988/89, 14, 259–306 
  7. [7] Neubrunnová A., On quasicontinuous and cliquishfunctions, Časopis Pěst. Mat., 1974, 99, 109–114 Zbl0292.26005
  8. [8] Stronska E., Maximal families for the class of upper and lower semi-quasicontinuous functions, Real Anal. Exchange, 2001/2002, 27, 599–608 Zbl1068.26009

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