Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Insertion; strong binary relation; Baire-$.5$ function; kernel of sets; lower cut set.
Insertion; strong binary relation; Baire-$.5$ function; kernel of sets; lower cut set.
Summary:
Necessary and sufficient conditions in terms of lower cut sets are given for the insertion of a Baire-$.5$ function between two comparable real-valued functions on the topological spaces that $F_{\sigma }$-kernel of sets are $F_{\sigma }$-sets.
References:
[1] Al-Omari, A., Noorani, M.S. Md: Some properties of contra-$b$-continuous and almost contra-$b$-continuous functions. European J. Pure. Appl. Math., 2, 2, 2009, 213-230, MR 2533786
[2] Brooks, F.: Indefinite cut sets for real functions. Amer. Math. Monthly, 78, 1971, 1007-1010, DOI 10.1080/00029890.1971.11992929 | MR 0306410
[3] Caldas, M., Jafari, S.: Some properties of contra-$\beta $-continuous functions. Mem. Fac. Sci. Kochi. Univ., 22, 2001, 19-28, MR 1822061
[4] Dontchev, J.: The characterization of some peculiar topological space via $\alpha $- and $\beta $-sets. Acta Math. Hungar., 69, 1--2, 1995, 67-71, DOI 10.1007/BF01874608 | MR 1339572
[5] Dontchev, J.: Contra-continuous functions and strongly $S$-closed space. Internat. J. Math. Math. Sci., 19, 2, 1996, 303-310, DOI 10.1155/S0161171296000427 | MR 1375993
[6] Dontchev, J., Maki, H.: On sg-closed sets and semi-$\lambda $-closed sets. Questions Answers Gen. Topology, 15, 2, 1997, 259-266, MR 1472189
[7] Ekici, E.: On contra-continuity. Annales Univ. Sci. Bodapest, 47, 2004, 127-137, MR 2173828
[8] Ekici, E.: New forms of contra-continuity. Carpathian J. Math., 24, 1, 2008, 37-45, MR 2410204
[9] El-Magbrabi, A.I.: Some properties of contra-continuous mappings. Int. J. General Topol., 3, 1--2, 2010, 55-64,
[10] Ganster, M., Reilly, I.: A decomposition of continuity. Acta Math. Hungar., 56, 3--4, 1990, 299-301, DOI 10.1007/BF01903846 | MR 1111316
[11] Jafari, S., Noiri, T.: Contra-continuous function between topological spaces. Iranian Int. J. Sci., 2, 2001, 153-167, MR 1880833
[12] Jafari, S., Noiri, T.: On contra-precontinuous functions. Bull. Malaysian Math. Sc. Soc., 25, 2002, 115-128, MR 1999994
[13] Katětov, M.: On real-valued functions in topological spaces. Fund. Math., 38, 1951, 85-91, DOI 10.4064/fm-38-1-85-91 | MR 0050264 | Zbl 0045.25704
[14] Katětov, M.: Correction to ``On real-valued functions in topological spaces". Fund. Math., 40, 1953, 203-205, DOI 10.4064/fm-40-1-203-205 | MR 0060211
[15] Lane, E.: Insertion of a continuous function. Pacific J. Math., 66, 1976, 181-190, DOI 10.2140/pjm.1976.66.181 | MR 0474186
[16] Maheshwari, S.N., Prasad, R.: On $R_{Os}$-spaces. Portugal. Math., 34, 1975, 213-217, MR 0410661
[17] Maki, H.: Generalized $\Lambda $-sets and the associated closure operator. The special Issue in commemoration of Prof. Kazuada IKEDA's Retirement, 1986, 139-146,
[18] Mrsevic, M.: On pairwise $R$ and pairwise $R_1$ bitopological spaces. Bull. Math. Soc. Sci. Math. R. S. Roumanie, 30, 1986, 141-145, MR 0850100
[19] Nasef, A.A.: Some properties of contra-continuous functions. Chaos Solitons Fractals, 24, 2005, 471-477, DOI 10.1016/j.chaos.2003.10.033 | MR 2114437
[20] Przemski, M.: A decomposition of continuity and $\alpha $-continuity. Acta Math. Hungar., 61, 1--2, 1993, 93-98, DOI 10.1007/BF01872101 | MR 1200962
[21] Rosen, H.: Darboux Baire-$.5$ functions. Proc. Amer. math. Soc., 110, 1, 1990, 285-286, MR 1017851
[22] Stone, M.H.: Boundedness properties in function-lattices. Canad. J. Math, 1, 1949, 176-189, DOI 10.4153/CJM-1949-016-5 | MR 0029091 | Zbl 0032.16901
Search
Partner of
