Title:
|
Insertion of a Contra-Baire-$1$ (Baire-$.5$) Function (English) |
Author:
|
Mirmiran, Majid |
Language:
|
English |
Journal:
|
Communications in Mathematics |
ISSN:
|
1804-1388 (print) |
ISSN:
|
2336-1298 (online) |
Volume:
|
27 |
Issue:
|
2 |
Year:
|
2019 |
Pages:
|
89-101 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
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. (English) |
Keyword:
|
Insertion |
Keyword:
|
strong binary relation |
Keyword:
|
Baire-$.5$ function |
Keyword:
|
kernel of sets |
Keyword:
|
lower cut set. |
MSC:
|
26A15 |
MSC:
|
54C30 |
idZBL:
|
Zbl 1470.26005 |
idMR:
|
MR4058168 |
. |
Date available:
|
2020-02-20T08:59:12Z |
Last updated:
|
2021-11-01 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147984 |
. |
Reference:
|
[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 |
Reference:
|
[2] Brooks, F.: Indefinite cut sets for real functions.Amer. Math. Monthly, 78, 1971, 1007-1010, MR 0306410, 10.1080/00029890.1971.11992929 |
Reference:
|
[3] Caldas, M., Jafari, S.: Some properties of contra-$\beta $-continuous functions.Mem. Fac. Sci. Kochi. Univ., 22, 2001, 19-28, MR 1822061 |
Reference:
|
[4] Dontchev, J.: The characterization of some peculiar topological space via $\alpha $- and $\beta $-sets.Acta Math. Hungar., 69, 1--2, 1995, 67-71, MR 1339572, 10.1007/BF01874608 |
Reference:
|
[5] Dontchev, J.: Contra-continuous functions and strongly $S$-closed space.Internat. J. Math. Math. Sci., 19, 2, 1996, 303-310, MR 1375993, 10.1155/S0161171296000427 |
Reference:
|
[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 |
Reference:
|
[7] Ekici, E.: On contra-continuity.Annales Univ. Sci. Bodapest, 47, 2004, 127-137, MR 2173828 |
Reference:
|
[8] Ekici, E.: New forms of contra-continuity.Carpathian J. Math., 24, 1, 2008, 37-45, MR 2410204 |
Reference:
|
[9] El-Magbrabi, A.I.: Some properties of contra-continuous mappings.Int. J. General Topol., 3, 1--2, 2010, 55-64, |
Reference:
|
[10] Ganster, M., Reilly, I.: A decomposition of continuity.Acta Math. Hungar., 56, 3--4, 1990, 299-301, MR 1111316, 10.1007/BF01903846 |
Reference:
|
[11] Jafari, S., Noiri, T.: Contra-continuous function between topological spaces.Iranian Int. J. Sci., 2, 2001, 153-167, MR 1880833 |
Reference:
|
[12] Jafari, S., Noiri, T.: On contra-precontinuous functions.Bull. Malaysian Math. Sc. Soc., 25, 2002, 115-128, MR 1999994 |
Reference:
|
[13] Katětov, M.: On real-valued functions in topological spaces.Fund. Math., 38, 1951, 85-91, Zbl 0045.25704, MR 0050264, 10.4064/fm-38-1-85-91 |
Reference:
|
[14] Katětov, M.: Correction to ``On real-valued functions in topological spaces".Fund. Math., 40, 1953, 203-205, MR 0060211, 10.4064/fm-40-1-203-205 |
Reference:
|
[15] Lane, E.: Insertion of a continuous function.Pacific J. Math., 66, 1976, 181-190, MR 0474186, 10.2140/pjm.1976.66.181 |
Reference:
|
[16] Maheshwari, S.N., Prasad, R.: On $R_{Os}$-spaces.Portugal. Math., 34, 1975, 213-217, MR 0410661 |
Reference:
|
[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, |
Reference:
|
[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 |
Reference:
|
[19] Nasef, A.A.: Some properties of contra-continuous functions.Chaos Solitons Fractals, 24, 2005, 471-477, MR 2114437, 10.1016/j.chaos.2003.10.033 |
Reference:
|
[20] Przemski, M.: A decomposition of continuity and $\alpha $-continuity.Acta Math. Hungar., 61, 1--2, 1993, 93-98, MR 1200962, 10.1007/BF01872101 |
Reference:
|
[21] Rosen, H.: Darboux Baire-$.5$ functions.Proc. Amer. math. Soc., 110, 1, 1990, 285-286, MR 1017851 |
Reference:
|
[22] Stone, M.H.: Boundedness properties in function-lattices.Canad. J. Math, 1, 1949, 176-189, Zbl 0032.16901, MR 0029091, 10.4153/CJM-1949-016-5 |
. |