On spaces of transfinite dimension (Q1358581)

The author studies the transfinite dimension \(\text{trdim }X\) which was introduced by \textit{P. Borst} [Fundam. Math. 130, No. 1, 1-25 (1988; Zbl 0661.54035)]. The main result of the paper is a collective factorization theorem for \(\text{trdim }X\) (where \(X\) is an arbitrary normal space) which generalizes an earlier result of \textit{A. V. Zarelua} [Sov. Math., Dokl. 3, 800-803 (1962); translation from Dokl. Akad. Nauk SSSR 144, 713-716 (1962; Zbl 0119.38205)] and the standard factorization theorem for \(\text{trdim }X\). This answers in affirmative a question due to B. A. Pasynkov.