2 problems

Let $M$ be a manifold, let $l$ be a positive integer, and let $k_1,\ldots,k_l$ be degrees. For a cover $\mathcal{U}$ of $M^l$, suppose that every intersection of elements of…

Let $X$ be a Peano continuum, that is, a compact, connected, locally connected metrizable space. For a compatible metric $d$ on $X$, let $\hat{H}_d$ denote the associated metric-de…