On conforming axiomatics (Q1570915)

Some new axioms are considered for dimension functions defined on the class of compact metrizable or separable metrizable spaces, such as (1) If there exists a decomposing mapping \(f:X\to Y\) [\textit{A. V. Zarelua}, Sov. Math., Dokl. 3, 800-803 (1962); translation from Dokl. Akad Nauk SSSR 144, 713-716 (1962; Zbl 0119.38205)], then \(d(X)\leq d(Y)\), and (2) If \(X\)is non-degenerate and \(d(X)\geq 0\), then there is a partition \(Y\) in \(X\) with \(d(Y)\leq d(X)-1\). Axiomatic characterizations are obtained for the covering dimension dim, its transfinite extension introduced by \textit{D. W. Henderson} [Pac. J. Math. 26, 91-107 (1968; Zbl 0162.26904)], and a transfinite extension introduced by the author.