On Fuzzy F ∗ -Simply Connected Spaces in Fuzzy F ∗ -Homotopy

Abstract

In this paper, the notions of fuzzy ${\mathcal{F}}^{\ast }$ -simply connected spaces and fuzzy ${\mathfrak{F}}^{\ast }$ -structure homeomorphisms are introduced, and further fuzzy ${\mathfrak{F}}^{\ast }$ -structure homeomorphism between fuzzy ${\mathfrak{F}}^{\ast }$ -path-connected spaces are studied. Also, it is shown that every fuzzy ${\mathcal{F}}^{\ast }$ -structure subspace of fuzzy ${\mathcal{F}}^{\ast }$ -simply connected space is fuzzy ${\mathcal{F}}^{\ast }$ -simply connected subspace. Further, the concepts of fuzzy ${\mathcal{F}}^{\ast }$ -contractible spaces and fuzzy ${\mathcal{F}}^{\ast }$ -retracts are introduced, and it is proved that every fuzzy ${\mathcal{F}}^{\ast }$ -contractible space is fuzzy ${\mathcal{F}}^{\ast }$ -simply connected.