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Functionally Separation Axioms on General Topology

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  • Abdelwaheb Mhemdi
  • Tareq M. Al-shami
  • Jia-Bao Liu

Abstract

In this paper, we define a new family of separation axioms in the classical topology called functionally Ti spaces for i=0,1,2. With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with Ti spaces for i=0,1,2. We demonstrate that functionally Ti spaces are preserved under product spaces, and they are topological and hereditary properties. Moreover, we show that the class of each one of them represents a transitive relation and obtain some interesting results under some conditions such as discrete and Sierpinski spaces.

Suggested Citation

  • Abdelwaheb Mhemdi & Tareq M. Al-shami & Jia-Bao Liu, 2021. "Functionally Separation Axioms on General Topology," Journal of Mathematics, Hindawi, vol. 2021, pages 1-5, May.
    • Handle: RePEc:hin:jjmath:5590047
    DOI: 10.1155/2021/5590047
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