Geodesic
Triples of infinite iterates of metrizable functors
Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 411-433.

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The concepts of metrizable, uniformly metrizable, and perfectly metrizable functors are introduced. The triple $\mathscr F^+$, $\mathscr F^{++}$, $\mathscr F^\omega$ of infinite iterates of a perfectly metrizable functor $\mathscr F$ is defined. The geometric properties of such triples are investigated for the continuous hyperspace functor and the probability measure functor. 
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V. V. Fedorchuk. Triples of infinite iterates of metrizable functors. Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 411-433. http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a9/

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