‎INSERTION OF A CONTRA-CONTINUOUS FUNCTION BETWEEN TWO ‎‎COMPARABLE CONTRA-$\alpha-$CONTINUOUS (CONTRA-$C-$CONTINUOUS) FUNCTIONS

Majid Mirmiran, Binesh Naderi

DOI Number
https://doi.org/10.22190/FUMI1901013M
First page
13
Last page
22

Abstract


‎A necessary and sufficient condition in terms of lower cut sets ‎are given for the insertion of a contra-continuous function ‎between two comparable real-valued functions on such topological ‎spaces that kernel of sets are open‎.

 


Keywords

‎Insertion‎, ‎Strong binary relation‎, ‎$C-$open set‎, ‎Semi-preopen set‎, ‎$\alpha-$open set‎, ‎Contra-continuous function‎, ‎Lower cut set.

Keywords


‎Insertion‎, ‎Strong binary relation‎, ‎$C-$open set‎, ‎Semi-preopen set‎, ‎$\alpha-$open set‎, ‎Contra-continuous function‎, ‎Lower cut set‎

Full Text:

PDF

References


‎{1} A‎. ‎Al-Omari and M.S‎. ‎Md Noorani‎, ‎Some properties of contra-b-continuous and almost contra-b-continuous functions‎, ‎European J‎. ‎Pure‎. ‎Appl‎. ‎Math.‎, ‎2(2)(2009)‎, ‎213-230‎.

‎{2} F‎. ‎Brooks‎, ‎Indefinite cut sets for real functions‎,

‎Amer‎. ‎Math‎. ‎Monthly‎, ‎78(1971)‎, ‎1007-1010‎.

‎{3} M‎. ‎Caldas and S‎. ‎Jafari‎, ‎Some properties of contra-$beta-$continuous functions‎, ‎Mem‎. ‎Fac‎. ‎Sci‎. ‎Kochi‎. ‎Univ.‎, ‎22(2001)‎, ‎19-28‎.

‎{4} J‎. ‎Dontchev‎, ‎The characterization of some peculiar‎

‎topological space via $alpha-$ and $beta-$sets‎, ‎Acta Math‎.

‎Hungar.‎, ‎69(1-2)(1995)‎, ‎67-71‎.

‎{5} J‎. ‎Dontchev‎, ‎Contra-continuous functions and strongly‎

‎S-closed space‎, ‎Intrnat‎. ‎J‎. ‎Math‎. ‎Math‎. ‎Sci.‎, ‎19(2)(1996)‎,

‎303-310‎.

‎{6} J‎. ‎Dontchev‎, ‎and H‎. ‎Maki‎, ‎On sg-closed sets and‎

‎semi$-lambda-$closed sets‎, ‎Questions Answers Gen‎. ‎Topology‎,

‎15(2)(1997)‎, ‎259-266‎.

‎{7} J‎. ‎Dontchev‎, ‎Between $alpha-$ and $beta-$sets‎, ‎Math‎.

‎Balkanica (N.S)‎, ‎12(3-4)(1998)‎, ‎295-302‎.

‎{8} E‎. ‎Ekici‎, ‎On contra-continuity‎, ‎Annales Univ‎. ‎Sci‎. ‎Bodapest‎, ‎47(2004)‎, ‎127-137‎.

‎{9} E‎. ‎Ekici‎, ‎New forms of contra-continuity‎, ‎Carpathian J‎. ‎Math.‎, ‎24(1)(2008)‎, ‎37-45‎.

‎{10} A.I‎. ‎El-Magbrabi‎, ‎Some properties of contra-continuous mappings‎, ‎Int‎. ‎J‎. ‎General Topol.‎, ‎3(1-2)(2010)‎, ‎55-64‎.

‎{11} M‎. ‎Ganster and I‎. ‎Reilly‎, ‎A decomposition of continuity‎, ‎Acta Math‎. ‎Hungar.‎, ‎56(3-4)(1990)‎,

‎299-301‎.

‎{12} E‎. ‎Hatir‎, ‎T‎. ‎Noiri and S‎. ‎Yksel‎, ‎A decomposition of‎

‎continuity‎, ‎Acta Math‎. ‎Hungar.‎, ‎70(1-2)(1996)‎, ‎145-150‎.

‎{13} S‎. ‎Jafari and T‎. ‎Noiri‎, ‎Contra-continuous function between topological spaces‎, ‎Iranian Int‎. ‎J‎. ‎Sci.‎, ‎2(2001)‎, ‎153-167‎.

‎{14} S‎. ‎Jafari and T‎. ‎Noiri‎, ‎On contra-precontinuous functions‎, ‎Bull‎. ‎Malaysian Math‎. ‎Sc‎. ‎Soc.‎, ‎25(2002)‎, ‎115-128‎.

‎{15} M‎. ‎Katv{e}tov‎, ‎On real-valued functions‎

‎in topological spaces‎, ‎Fund‎. ‎Math.‎, ‎38(1951)‎, ‎85-91‎.

‎{16} M‎. ‎Katv{e}tov‎, ‎Correction to‎, "‎On‎

‎real-valued functions in topological spaces"‎, ‎Fund‎. ‎Math.‎,

‎40(1953)‎, ‎203-205‎.

‎{17} E‎. ‎Lane‎, ‎Insertion of a continuous function‎, ‎Pacific‎

‎J‎. ‎Math.‎, ‎66(1976)‎, ‎181-190‎.

‎{18} S‎. ‎N‎. ‎Maheshwari and R‎. ‎Prasad‎, ‎On $R_{Os}-$spaces‎,

‎Portugal‎. ‎Math.‎, ‎34(1975)‎, ‎213-217‎.

‎{19} H‎. ‎Maki‎, ‎Generalized $Lambda-$sets and the associated‎

‎closure operator‎, ‎The special Issue in commemoration of Prof‎.

‎Kazuada IKEDA's Retirement‎, ‎(1986)‎, ‎139-146‎.

‎{20} M‎. ‎Mirmiran‎, ‎Insertion‎

‎of a function belonging to a certain subclass of $mathbb{R}^X$‎,

‎Bull‎. ‎Iran‎. ‎Math‎. ‎Soc.‎, ‎28(2)(2002)‎, ‎19-27‎.

‎{21} M‎. ‎Mrsevic‎, ‎On pairwise $R$ and pairwise $R_1$ bitopological spaces‎, ‎Bull‎. ‎Math‎. ‎Soc‎. ‎Sci‎. ‎Math‎. ‎R‎. ‎S‎. ‎Roumanie‎, ‎30(1986)‎, ‎141-145‎.

‎{22} A.A‎. ‎Nasef‎, ‎Some properties of contra-continuous functions‎, ‎Chaos Solitons Fractals‎, ‎24(2005)‎, ‎471-477‎.

‎{23} M‎. ‎Przemski‎, ‎A decomposition of continuity and $alpha-$continuity‎, ‎Acta Math‎. ‎Hungar.‎, ‎61(1-2)(1993)‎, ‎93-98‎.




DOI: https://doi.org/10.22190/FUMI1901013M

Refbacks





© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)