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...

It is possible for one to define fractals as those sets which have non-integral Hausdorff Dimension. This paper defines Hausdorff Dimension and rigorously introduces the necessary theory to prove that one such set is indeed a fractal. The first chapter includes a proof of Banach’s Fixed Point Theorem. The Hausdorff Metric is defined and it is mentioned how one produces ‘generators’ for creating...

Let B = {b1, . . . , bK} denote a set of pure outcomes. Let ∆(B) denote the set of probability distributions on B. Finally, let denote a preference relation on the set of nonempty subsets of ∆(B) where this space is endowed with the Hausdorff topology. Let dh(x, y) denote the Hausdorff distance between x and y. ∗Economics Dept., Northwestern University, and School of Economics, Tel Aviv Univers...