Axiomatic characterizations of dimension in special classes of spaces (Q2703101)

This paper contains proofs of two axiomatic characterizations of dimension as well as of the independence of the relevant axioms. In the first, for the class of separable metrizable spaces, the dimension function is required to be topologically invariant, normed, \(F_\sigma\)-constant, \(G_\delta\)-enlargeable and to satisfy Hayashi's decomposition axiom. In the second, for the class of all subspaces of \(\mathbb{R}^n\), \(n\geq 3\), an addition axiom is added while the property of being normed is required only in respect of \(\emptyset\), \(\{0\}\) and \([0,1]\).