Limits of Manifolds in the Gromov–Hausdorff Metric Space

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