α-separation axioms based on Lukasiewicz logic

Year 2014, Volume: 43 Issue: 2, 259 - 277, 01.04.2014

O.r. Sayed

Abstract

In the present paper, we introduce topological notions defined by means
of α-open sets when these are planted into the framework of Ying’s
fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T
α
0 −, T α
1 −, T α
2 (α- Hausdorff)-, T
α
3 (α-regular)- and T
α
4 (αnormal)-separation axioms. Furthermore, the R
α
0 − and R
α
1 − separation axioms are studied and their relations with the T
α
1 − and T
α
2 −
separation axioms are introduced. Moreover, we clarify the relations
of these axioms with each other as well as the relations with other
fuzzifying separation axioms.

Keywords

Lukasiewicz logic, semantics, fuzzifying topology, fuzzifying separation axioms, α-separation axioms

References

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