Weak Insertion of an α−Continuous Function
Mathematics Letters
Volume 2, Issue 3, June 2016, Pages: 25-27
Received: Aug. 23, 2016; Accepted: Oct. 12, 2016; Published: Oct. 19, 2016
Views 2564      Downloads 86
Author
Majid Mirmiran, Department of Mathematics, University of Isfahan, Isfahan, Iran
Article Tools
Follow on us
Abstract
A sufficient condition in terms of lower cut sets are given for the weak α−insertion property and the weak insertion of an α−continuous function between two comparable real-valued functions. Also several insertion theorems are obtained as corollaries of this result.
Keywords
Weak Insertion, Strong Binary Relation, Preopen Set, Semi-Open Set, α−Open Set, Lower Cut Set
To cite this article
Majid Mirmiran, Weak Insertion of an α−Continuous Function, Mathematics Letters. Vol. 2, No. 3, 2016, pp. 25-27. doi: 10.11648/j.ml.20160203.11
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
H. H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math, 8(1964), 351-360.
[2]
A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On pre-continuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
[3]
N. Levine, Semi-open sets and semi-continuity in topological space, Amer. Math. Monthly, 70(1963), 36-41.
[4]
M. Przemski, A decomposition of continuity and α−continuity, Acta Math. Hungar, 61(1-2)(1993), 93-98.
[5]
J. Dontchev, The characterization of some peculiar topological space via α− and β−sets, Acta Math. Hungar, 69(1-2)(1995), 67-71.
[6]
M. Ganster and I. Reilly, A decomposition of continuity, Acta Math. Hungar, 56(3-4)(1990), 299-301.
[7]
V. Ptk, Completeness and open mapping theorem, Bull. Soc. Math. France, 86(1958), 41-74.
[8]
T. Husain, Almost continuous mappings, Prace Mat, 10(1966), 1-7.
[9]
H. Blumberg, New properties of all functions, Trans. Amer. Math. soc., 24(1922), 113-128.
[10]
M. Katˇetov, On real-valued functions in topological spaces, Fund. Math, 38(1951), 85-91.
[11]
M. Katˇetov, Correction to, “On real-valued functions in topological spaces”, Fund. Math., 40(1953), 203-205.
[12]
F. Brooks, Indefinite cut sets for real functions, Amer. Math. Monthly, 78(1971), 1007-1010.
[13]
E. Lane, Insertion of a continuous function, Pacific J. Math, 66(1976), 181-190.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186