20.500.12556/RUL-143766 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 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. Gromov-Hausdorff metric Gromov topological moduli space manifold-like generalized manifold absolute neighborhood retract cell-like map $\delta$-map structure map controlled surgery sequence $\varepsilon$-homotopy 2-patch space $\varepsilon$-homotopy equivalence periodic surgery spectrum $\mathbb{L}$ true false true Angleški jezik Ni določen Članek v reviji 2023-01-11 13:02:12 2023-01-11 13:02:14 2023-05-18 13:34:56 0000-00-00 00:00:00 2023 0 0 11 str. iss. 1, art. 47 Vol. 20 Feb. 2023 0000-00-00 PostprintKoncna Objavljeno apc 0000-00-00 0000-00-00 0000-00-00 2024-02-01 515.14:514.7 1660-5446 10.1007/s00009-022-02250-9 135986179 RAZ_Hegenbarth_Friedrich_2023_(6).pdf RAZ_Hegenbarth_Friedrich_2023_(6).pdf 1 36463553151ADBE80C2F9CEA4D0EB524 54718c85b5250d6901f1c46b3037cb3ce33c2b4b381c720a5804fb14160d0895 070aa251-ea7e-11ed-a314-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=168618 https://link.springer.com/article/10.1007/s00009-022-02250-9 1 8efc932a-91a7-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=165676 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0