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 Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 2, Pages 396–417 (Mi izv1100)

Triples of infinite iterates of metrizable functors

V. V. Fedorchuk

Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:2, 411–433

Bibliographic databases:

UDC: 515.12
MSC: Primary 54B30, 54E45, 54E50; Secondary 54B20, 54C50, 54F25

Citation: V. V. Fedorchuk, “Triples of infinite iterates of metrizable functors”, Izv. Akad. Nauk SSSR Ser. Mat., 54:2 (1990), 396–417; Math. USSR-Izv., 36:2 (1991), 411–433

Citation in format AMSBIB
\Bibitem{Fed90} \by V.~V.~Fedorchuk \paper Triples of infinite iterates of metrizable functors \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1990 \vol 54 \issue 2 \pages 396--417 \mathnet{http://mi.mathnet.ru/izv1100} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1062520} \zmath{https://zbmath.org/?q=an:0715.54005} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..411F} \transl \jour Math. USSR-Izv. \yr 1991 \vol 36 \issue 2 \pages 411--433 \crossref{https://doi.org/10.1070/IM1991v036n02ABEH002028} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Fedorchuk, “Probability measures in topology”, Russian Math. Surveys, 46:1 (1991), 45–93
2. Vitaly V. Fedorchuk, Yury V. Sadovnichy, “On some categorical properties of uniform spaces of probability measures”, Topology and its Applications, 82:1-3 (1998), 131
3. V.V. Fedorchuk, “On a preservation of completeness of uniform spaces by the functor PscT”, Topology and its Applications, 91:1 (1999), 25
4. Yu. V. Sadovnichii, “Lifting the functors $U_\tau$ and $U_R$ to the categories of bounded metric spaces and uniform spaces”, Sb. Math., 191:11 (2000), 1667–1691
5. A. A. Zaitov, “Open Mapping Theorem for Spaces of Weakly Additive Homogeneous Functionals”, Math. Notes, 88:5 (2010), 655–660
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