9
votes
1answer
193 views

Why do convex polytope options constrict with dimension, rather than expand?

There are an infinite number of regular polygons in the plane, five regular polyhedra, six regular polytopes in $\mathbb{R}^4$, and then three regular polytopes in every dimension $d > 4$. There ...
4
votes
1answer
680 views

Example in dimension theory

Could you give me an example of a complete metric space wiht covering dimension $> n$ all of which compact subsets have covering dimension $\le n$?
4
votes
2answers
288 views

How indepenedent of a chosen metric is the box-counting dimension? Is there a non-integral dimension which is defined for topological spaces?

Question 1. Given a topological space $X$ and two metrics $a$ and $b$ on it, compatible with the topology, what conditions should I impose on them so that box-counting (or other, for example ...
3
votes
2answers
509 views

How big can the Hausdorff dimension of a function graph get?

This question is inspired by How kinky can a Jordan curve get? What is the least upper bound for the Hausdorff dimension of the graph of a real-valued, continuous function on an interval? Is the ...