Let dim $X$ denote the Lebesgue covering dimension for a topological space $X$. Now a result in common books concerning dimension theory states the following: If $X$ is a normal topological space, then 1) dim $X\leq n$ if and only if 2) every continuous function $f : X → {\mathbb{R}}^{n+1}...

The word covering has various meanings in mathematics. Quite often choosing a tag-name which has several unrelated meanings can lead to problems - typically bunch of rather unrelated questions end up under the same tag. Probably the most common meanings are covering spaces and covering maps in a...