Given any non-trivial, connected topological space X, it is possible to define an equivalence relation ∼ on it such that the topological quotient space X/ ∼ is the Sierpinski space. Locally Sierpinski spaces are generalizations of the Sierpinski space and here we address the following question. Does a statement like the one above hold if Sierpinski is replaced by (proper) locally Sierpinski ? T...

We define the manifold of configurations to be quotient set k points in Euclidean space identified under congruence, and prove that compact subsets ℝd, d≥2, large Hausdorff dimension have a non-null them. Our method simplifies previous work achieves better dimensional threshold.