We apply the Gromov-Hausdorff metric ▫$d_G$▫ for characterization of certain generalized manifolds. Previously, we have proven that with respect to the metric ▫$d_G$▫, generalized ▫$n$▫-manifolds are ...limits of spaces which are obtained by gluing two topological ▫$n$▫-manifolds by a controlled homotopy equivalence (the so-called 2-patch spaces). In the present paper, we consider the so-called manifold-like generalized ▫$n$▫-manifolds ▫$X^{n}$▫, introduced in 1966 by Mardeić and Segal, which are characterized by the existence of ▫$\delta$▫-mappings ▫$f_{\delta }$▫ of ▫$X^{n}$▫ onto closed manifolds ▫$M^{n}_{\delta }$▫, for arbitrary small ▫$\delta >0$▫, i.e., there exist onto maps ▫$f_{\delta }:X^{n}\rightarrow M^{n}_{\delta}$▫ such that for every ▫$M^{n}_{\delta }$▫, ▫$f^{-1}_{\delta }(u)$▫ has diameter less than ▫$\delta$▫. We prove that with respect to the metric ▫$d_G$▫, manifold-like generalized ▫$n$▫-manifolds ▫$X^{n}$▫ are limits of topological ▫$n$▫-manifolds ▫$M^{n}_{i}$▫. Moreover, if topological ▫$n$▫-manifolds ▫$M^{n}_{i}$▫ satisfy a certain local contractibility condition ▫${\mathcal {M}}(\varrho, n)$▫, we prove that generalized ▫$n$▫-manifold ▫$X^{n}$▫ is resolvable.
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https://link.springer.com/article/10.1007/s00009-022-02250-9
