Limits of manifolds in the Gromov-Hausdorff metric spaceHegenbarth, Friedrich (Avtor) Repovš, Dušan (Avtor) Gromov-Hausdorff metricGromov topological moduli spacemanifold-like generalized manifoldabsolute neighborhood retractcell-like map$\delta$-mapstructure mapcontrolled surgery sequence$\varepsilon$-homotopy2-patch space$\varepsilon$-homotopy equivalenceperiodic surgery spectrum $\mathbb{L}$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 $u \in M^{n}_{\delta }$, $f^{-1}_{\delta }(u)$ 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.20232023-01-11 13:02:12Članek v reviji143766sl