On α − and α *− T0 and T1 Separation Axioms In I− Fuzzy Topological Spaces
Keywords:
α − T0, α* − T0, α − T1, α* − T1.Abstract
Sostak and Kubiak introduced I−fuzzy topological spaces. Subspaces and products of I−fuzzy topological spaces have been introduced and studied by Peeters and ˇ Sostak. Srivastava et al. introduced and studied α− and α*−Hausdorff I−fuzzy topological space. George and Veeramani improved the definition of a fuzzy metric, which was first introduced by Kramosil and Mich´alek. Grecova et al. constructed an LM−fuzzy topological space using a strong fuzzy metric, where L and M are complete sublattices of the unit interval [0,1] containing 0 and 1. This LM−fuzzy topological space reduces to an I− fuzzy topological space if L = M = I = [0, 1]. In this paper, we have introduced α − T0, α* − T0, α − T1 and α* − T1 separation axioms in I−fuzzy topological spaces and established several basic desirable results. In particular, it has been proved that these separation axioms satisfy the hereditary, productive and projective properties. Further, we have proved that in an I−fuzzy topological space, α−Hausdorff⇒ α−T1 ⇒ α−T0 and α*−Hausdorff⇒ α* − T1 ⇒ α* − T0. It has been also shown that an I−fuzzy topological space induced by a strong fuzzy metric is α−Hausdorff, for α ∈ [0, 1) and α*−Hausdorff, for α ∈ (0, 1], which further implies that this I−fuzzy topological space satisfies α − T0, α* − T0, α − T1 and α* − T1 separation axioms.
Key words and phrases. α − T0, α* − T0, α − T1, α* − T1.
2010 Mathematics Subject Classification. 54A40, 54D10
