On fuzzy \(\mathfrak{F}^\ast \)-simply connected spaces in fuzzy \(\mathfrak{F}^\ast\)-homotopy (Q2672557)

Summary: 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.