On some spaces which can be partitioned by the rational line (Q1058179)

A space X partitions a space Y if Y can be covered by pairwise disjoint homeomorphs of X. This concept was introduced by the reviewer and \textit{R. J. McGovern} [General Topol. Appl. 10, 215-229 (1979; Zbl 0406.50002)] where it was proved that the rational line partitions any space which is \(T_ 3\), first countable, self-dense, and hereditarily Lindelöf (a self-dense separable metrizable space, say). There the question was raised whether every self-dense metrizable space could be so partitioned, and an affirmative answer came forth in the author's paper in Topology Appl. 12, 331-332 (1981; Zbl 0454.54004)]. The author extends all versions of the above result which were previously known: the rational line partitions any space which is \(T_ 3\), first countable, self-dense, and hereditarily pointwise para-Lindelöf.