Previous |  Up |  Next

Article

Keywords:
separate almost continuity; almost quasicontinuous functions; almost quasicontinuity; $\beta$-continuity; separate almost quasicontinuity
Summary:
A function $f:X\rightarrow Y$ is said to be almost quasicontinuous at $x\in X$ if $x\in C\left| Int C\right|f^{-1}(V)$ for each neighbourhood $V$ of $f(x)$. Some properties of these functions are investigated.
References:
[1] M. E. Abd El-Monsef S. N. El-Deeb R. A. Mahmoud: $\beta$-open sets and $\beta$-continuous mappings. Bull. Fac. Sci. Assiut Univ. 12 (1983), 77-90. MR 0828081
[2] D. Andrijevic: Semi-preopen sets. Mat. Vesnik 38 (1986), 24-32. Zbl 0604.54002
[3] J. Borsík J. Doboš: On decomposition of quasicontinuity. Real Anal. Exchange 16 (1990-91), 292-305. DOI 10.2307/44153699 | MR 1087494
[4] A. M. Bruckner: Differentiation of real functions. Springer-Verlag, Berlin-Heidelberg-New York, 1978. MR 0507448 | Zbl 0382.26002
[5] Z. Frolík: Remarks concerning the invariance of Baire spaces under mappings. Czechoslovak Math. J. 11 (1961), 381-385. MR 0133098
[6] K. R. Gentry H. B. Hoyle: Somewhat continuous functions. Czechoslovak Math. J. 21 (1971), 5-12. MR 0278269
[7] T. Husain: Almost continuous mappings. Comment. Math 10 (1966), 1-7. MR 0220256 | Zbl 0138.17601
[8] N. Levine: Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly 70 (1963), 36-41. DOI 10.1080/00029890.1963.11990039 | MR 0166752 | Zbl 0113.16304
[9] S. Marcus: Sur les fonctions quasicontinues au sens de S. Kempisty. Colloq. Math. 8 (1961), 47-53. DOI 10.4064/cm-8-1-47-53 | MR 0125915 | Zbl 0099.04501
[10] A. S. Mashour M. E. Abd Ei-Monsef S. N. El-Deeb: On precontinuous and weak precontinuous mappings. Pгoc. Math. Phys. Soc. Egypt 53 (1982), 47-53. MR 0830896
[11] O. Náther T. Neubrunn: On characterization of quasicontinuous multifunctions. Časopis Pěst. mat. 107 (1982), 294-300. MR 0673055
[12] T. Neubrunn: A generalized continuity and product spaces. Math. Slovaca 26 (1976), 97-99. MR 0436064 | Zbl 0318.54008
[13] T. Neubrunn: Generalized continuity and separate continuity. Math. Slovaca 27 (1977), 307-314. MR 0536149 | Zbl 0371.54022
[14] A. Neubrunnová: On certain generalizations of the notion of continuity. Mat. časopis 23 (1973), 374-380. MR 0339051
[15] A. Neubrunnová T. Šalát: On almost quasicontinuity. Math. Bohemica 117 (1992), 197-205. MR 1165897
[16] T. Noiri V. Popa: Weak forms of faint continuity. Bull. Math. Soc. Sci. Math. Roumanie З4 (1990), 263-270. MR 1087163
[17] J. C. Oxtoby: Cartesian product of Baire spaces. Fund. Math. 49 (1961), 156-170. MR 0140638
[18] Z. Piotrowski: A survey of results concerning generalized continuity in topological spaces. Acta Math. Univ. Comenian. 52-53 (1987), 91-110. MR 0989626
Partner of
EuDML logo