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Weak Insertion of an α−Continuous Function

Received: 23 August 2016     Accepted: 12 October 2016     Published: 19 October 2016
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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.

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

Keywords

Weak Insertion, Strong Binary Relation, Preopen Set, Semi-Open Set, α−Open Set, Lower Cut Set

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.
Cite This Article
  • 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

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    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

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    AMA Style

    Majid Mirmiran. Weak Insertion of an α−Continuous Function. Math Lett. 2016;2(3):25-27. doi: 10.11648/j.ml.20160203.11

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  • @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}
    }
    

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    T1  - Weak Insertion of an α−Continuous Function
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    N1  - https://doi.org/10.11648/j.ml.20160203.11
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    JF  - Mathematics Letters
    JO  - Mathematics Letters
    SP  - 25
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    PB  - Science Publishing Group
    SN  - 2575-5056
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    VL  - 2
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    ER  - 

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Author Information
  • Department of Mathematics, University of Isfahan, Isfahan, Iran

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