Home / Journals Pure and Applied Mathematics Journal / Decompositions of Continuous in Topological Spaces
Decompositions of Continuous in Topological Spaces
Submission DeadlineJan. 15, 2020

Submission Guidelines: http://www.sciencepublishinggroup.com/home/submission

Lead Guest Editor
Mustafa H. Hadi
Department of Mathematics, Faculty of Education for Pure Sciences, University of Babylon, Babylon - Hilla, Iraq
Guest Editors
  • Luay A.AL.Swidi
    Department of Mathematics, Faculty of Education for Pure Sciences, University of Babylon, Babylon - Hilla, Iraq
  • Ali Younis Shakir
    Department of Mathematics, Faculty of Education for Pure Sciences, University of Babylon, Babylon - Hilla, Iraq
  • Rabiha S. Kareem
    Department of Mathematics, Baghdad University, Baghdad, Iraq
  • Ahmed M. Abdulhadi
    Department of Mathematics, Faculty of Education for Pure Science, University of Baghdad, Baghdad, Iraq
  • Qays Hatem Imran
    Department of Mathematics, College of Education for Pure Science Al-Muthanna University, Samawah, Iraq
  • Murtadha M. Abdulkadhim
    Department of Mathematics, College of Education for Pure Science Al-Muthanna University, Samawah, Iraq
  • Sameer A. AL-Fathly
    Department of Mathematics, Faculty of Education for Pure Science, University of Babylon, Karbala, Iraq
  • Volety Venkata Satya Ramachandram
    Department of Science and Humanities, B V C College of Engineering, Rajahmundry, Andhrapradesh, India
Introduction
In 1982 the ω-closed set was first introduced by H. Z. Hdeib and he defined it as Definition 1. A sub set of any topological space is ω-closed if it contains all its condensation points and the ω-open set is the complement of the ω-closed set.
Levine introduced the definition of the generalized closed set. And he defined it as follows Definition 2. A sub set A of any topological space is called generalized closed set if cl(A)⊆U whenever A⊆U and U is open, where cl(A) is the closure of the set A.
Modefining Definition2 by using Definition1 we get a new type of generalized closed set call it the generalized ω-closed set (g- ω-closed). Define it as follows Definition 3. A sub set A of any topological space is called generalized ω-closed set (g- ω-closed) if 〖cl〗_ω (A)⊆U whenever A⊆U and U is ω-open set, where 〖cl〗_ω (A) is the ω-closure of the set A.
By making use of the generalized ω-closed set above we can define new types of weak continuities such as approximately ω-continuity, ultra ω-continuity, as follows Definition 4. A map f:X⟶Y is said to be approximately ω-continuous if 〖cl〗_ω (F)⊆f^(-1) (U), whenever U is ω-open subset of Y and F is g- ω-closed subset of X such that F⊆f^(-1) (U).
Definition 5. A map f:X⟶Y is said to be ultraω-continuous if f^(-1) (V) is ω-closed set in X for each ω-open set V in Y.
Also we define new types of weak openness and closeness such as approximately ω-closed mapping, approximately ω-open mapping , ultra ω-closed mapping, and ultra ω-open mapping as follows Definition 6. A map f:X⟶Y is said to be approximately ω-closed if 〖f(U)⊆int〗_ω (V), whenever V is a generalized ω-open subset of Y, F is ω-closed subset of X and f(F)⊆V. We mean by〖int〗_ω (V) is the union of all ω-open subset of V.
Definition 7. A map f:X⟶Y is said to be approximately ω-open if 〖cl〗_ω (F)⊆f(U), , whenever U is an ω-open subset of X, F is a generalized ω-closed subset of Y and F⊆f(U).
Definition 8. A map f:X⟶Y is said to be ultra ω-closed if for every ω-closed subset A of X, f(A) is ω-open set in Y.
Definition 9. A map f:X⟶Y is said to be ultra ω-open if for every ω-open subset A of X, f(A) is ω-closed set in Y.
Using Definition 6, Definition 7, Definition 8, and Definition 9 above we can find and prove relationships between ultra ω-continuity and the approximately ω-continuity, ultra ω-closed mappings and the approximately ω-closed mappings, and the ultra ω-open mappings and the approximately ω-open mappings.By the Definitions of α-ω-open set, pre –ω-open set, b-ω-open set, and β-ω-open set defined by T. Noiri, A. Al-Omari, M. S. M. Noorani and Definition2, we can define generalized α-ω-closed set, generalized pre –ω-closed set, generalized b-ω-closed set, and generalized β-ω-closed set. And then use them to define other types of ultra, approximately weak types of continuity, openness and closeness. Then make use of them to find the relationships mentioned above.
Aims and Scope:
  1. ω-closed
  2. generalized ω-closed set
  3. approximation space
  4. ultraω-continuous
  5. approximately ω-open
  6. approximately ω-continuous
  7. approximately ω-closed
  8. ultra ω-open
Guidelines for Submission
Manuscripts should be formatted according to the guidelines for authors
(see: http://www.sciencepublishinggroup.com/journal/guideforauthors?journalid=141).

Please download the template to format your manuscript.

ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186