Jan 5, 2021 · For more on this, see k-Hausdorff spaces which is a weaker condition than being Hausdorff, but still implies that every compact subspace is closed. It is equivalent to the so …

Hausdorff dimension of Cantor set Ask Question Asked 13 years, 7 months ago Modified 4 years, 7 months ago

May 15, 2015 · A Hausdorff Space is one in which for every x and y in X with x does not equal y, there exists an open set containing x and an open set containing y within x and the …

Could someone explain the intuition behind the Hausdorff Measure and Hausdorff Dimension? The Hausdorff Measure is defined as the following: Let $(X,d)$ be a metric space. $\\forall S …

Let X be Hausdorff, then if $x\ne y$ there are neighborhoods $V_x$ and $V_y$ such that $V_x \cap V_y = \emptyset$. Therefore $V_x\times V_y \cap D=\emptyset$ and the complement of …

This phenomena can not occur in Hausdorff spaces (sequence converging to a set with more than a single element). This idea of gluing Hausdorff spaces together everywhere except for some …

There are non-Hausdorff spaces that are locally Euclidean; some people include them in the class of manifolds, and some prefer to exclude them by requiring a manifold to be Hausdorff. The …

Jun 11, 2021 · One of the supplementary problems from Schaum's General Topology states that if you have a compact subset of a Hausdorff space and a point not in the compact subset, there …

May 9, 2018 · To equate the lower Minkowski dimension and Hausdorff dimension, I would likely attempt to do this directly by constructing a suitable measure on the Cantor set and using the …

Jan 31, 2017 · Compact subsets of Hausdorff spaces are closed and closed subsets of compact spaces are compact.