A necessary and sufficient condition for the metricization of a topological space (i.e., that the space be homeomorphism to a metric space) was first given by P. S. Aleksandrovsk and P. S.nRumson in 1925. These authors, however, did not consider their solution of the metricization problem satisfactory (see fornexample2, p. 263, where this solution is called "not very suitable"), clearly because of the artificial nature of the condition contained therein. This artificiality is particularly evident from the fact that the fundamental metrification conditions for spaces with a countable basis, as well as for compact spaces, are not special cases of the general metricization theorem of P. S. Aleksandrovsk and P. S. Rumson. The numerous metricization theorems which were subsequently proposed by various other authors show no improvements over the Aleksandrov-Uryson theorem.
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