Geodesic
On Projectively Inductively Closed Subfunctors of the Functor $P$ of Probability Measures
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 88-95

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In the paper, we examine topological and dimensional properties of metric, Tychonoff, compact $C$-spaces under the action of the covariant subfunctor $P_{f}$ of the functor $P$ of probability measures in the category of metric, compact, paracompact spaces and continuous mappings into itself. We consider geometric properties of spaces under the action of the subfunctor $P_{f}$ of the functor $P$ of probability measures and show that this functor $P_{f}$ is an open $\sigma$-p.i.c. functor that preserves soft mappings and various types of topological spaces.
Keywords: functor, probability measure, Dirac measure, soft mapping, $C$-space, inductively closed functor, sigma inductively closed functors, Dugundji compactum. 
@article{INTO_2018_144_a9,
     author = {Sh. A. Ayupov and T. F. Zhuraev},
     title = {On {Projectively} {Inductively} {Closed} {Subfunctors} of the {Functor} $P$ of {Probability} {Measures}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {88--95},
     publisher = {mathdoc},
     volume = {144},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_144_a9/}
}
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Sh. A. Ayupov; T. F. Zhuraev. On Projectively Inductively Closed Subfunctors of the Functor $P$ of Probability Measures. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 88-95. http://geodesic.mathdoc.fr/item/INTO_2018_144_a9/