3 problems

Let $f\colon X\to Y$ be a map of finite-dimensional metrizable compacta. For integers $0\leq t\leq d\leq T\leq m$, $d-t+1\leq q$, and $\dim f+d+1\leq m$, define…

Let $f\colon X\to Y$ be a map of finite-dimensional compacta, and let $C(X,\mathbb R^m)$ denote the space of continuous maps from $X$ to $\mathbb R^m$ with the uniform topology. Fo…

Let $f\colon X\to Y$ be a map of finite-dimensional metrizable compacta, and let $C(X,\mathbb R^m)$ denote the space of continuous maps from $X$ to $\mathbb R^m$ with the uniform t…