On the Brouwer dimension of compact spaces (Q1810308)

This paper deals with the relation between \(\dim X\) and a so-called ``dimensionsgrad'' which is denoted by \(\text{Dg }X\) for any set \(X\). The goal of this paper is to prove \(\dim X\leq \text{Dg }X\) for an arbitrary compact space \(X\). The author also shows that the equality \(\dim X= \text{Dg }X\) does not hold even for a first countable compact space \(X\).