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.
| Published in | Mathematics Letters (Volume 2, Issue 3) |
| DOI | 10.11648/j.ml.20160203.11 |
| Page(s) | 25-27 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Weak Insertion, Strong Binary Relation, Preopen Set, Semi-Open Set, α−Open Set, Lower Cut Set
| [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. |
APA Style
Majid Mirmiran. (2016). Weak Insertion of an α−Continuous Function. Mathematics Letters, 2(3), 25-27. https://doi.org/10.11648/j.ml.20160203.11
ACS Style
Majid Mirmiran. Weak Insertion of an α−Continuous Function. Math. Lett. 2016, 2(3), 25-27. doi: 10.11648/j.ml.20160203.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ml.20160203.11,
author = {Majid Mirmiran},
title = {Weak Insertion of an α−Continuous Function},
journal = {Mathematics Letters},
volume = {2},
number = {3},
pages = {25-27},
doi = {10.11648/j.ml.20160203.11},
url = {https://doi.org/10.11648/j.ml.20160203.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160203.11},
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.},
year = {2016}
}
TY - JOUR T1 - Weak Insertion of an α−Continuous Function AU - Majid Mirmiran Y1 - 2016/10/19 PY - 2016 N1 - https://doi.org/10.11648/j.ml.20160203.11 DO - 10.11648/j.ml.20160203.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 25 EP - 27 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20160203.11 AB - 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. VL - 2 IS - 3 ER -
Information
Email: