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. 
@article{IM2_1991_36_2_a9,
     author = {V. V. Fedorchuk},
     title = {Triples of infinite iterates of metrizable functors},
     journal = {Izvestiya. Mathematics },
     pages = {411--433},
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     volume = {36},
     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a9/}
}
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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/