All Questions

Given a set of points $\{x_{k}\}_{k=0}^{m} \subset \mathbb{R}^n$, is it always possible to find a constant $c=c(m,n)>0$, depending only on the dimension $n$ and the number $m$, such that, after ...

Given a positive constant $0<\gamma<1$, does there exists integer $k_0>0$ such that for any integer $k\geq k_0$ the following holds?: For any $A\subseteq\left[0,1\right]^k$ with the measure ...

Sperner’s Lemma is often called the "combinatorial analog" of Brouwer’s Fixed Point Theorem, and similarly Tucker’s Lemma is often called the combinatorial analog of Borsuk–Ulam’s Theorem. We can ...

My question is very basic: where can I find a complete (and hopefully self-contained) proof of the classification of Platonic solids? In all the references that I found, they use Euler's formula $v-e+...

Possible Duplicate: The Klein bottle and the Heawood Conjecture It is well known that the Heawood Conjecture states that the bound for the number of colours which are sufficient to colour a map ...