Taibleson-Hirshmann Colloquium: Embeddings into Euclidean spaces without shrinking

Abstract: We study the problem which spaces $(X,\rho)$ can be embedded into $\mathbb R^d$ without decreasing any of the distances in X. That is, we ask the question whether there is an $f:X\to\mathbb R^d$ such that $\|x-y\|\ge\rho(x,y)$ for every $x,y\in X$. Our aim is to find necessary and sufficient conditions under which such a mapping exists, and to show how this can be used to generalize/disprove some classical results in real analysis.

Host: Alan Chang