Geodesic
Geometrical and topological properties of a subspace $P_f(X)$ of probability measures
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 28-37 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove that for a compact $X$ the space $P_{f}(X)$ is an absolute neighbourhood retract if and only if $X$ is an absolute neighbourhood retract. Futher, we demonstrate that a functor $P_{f}$ preserves the property of a compact to be $Q$-manifold or Hilbert cube, preserves the propetry of a map to be absolute neighbourhood retract in a class of compact, to be $Q$-manifold or Hilbetr cube (finite sum of Hilbert cube).
Keywords: propability measure, compact Hausdorff space (compact), $A(N)R$-space.
Mots-clés : retract 
@article{IVM_2019_10_a3,
     author = {A. A. Zaitov},
     title = {Geometrical and topological properties of a subspace $P_f(X)$ of probability measures},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {28--37},
     year = {2019},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_10_a3/}
}
TY  - JOUR
AU  - A. A. Zaitov
TI  - Geometrical and topological properties of a subspace $P_f(X)$ of probability measures
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 28
EP  - 37
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/IVM_2019_10_a3/
LA  - ru
ID  - IVM_2019_10_a3
ER  - 
%0 Journal Article
%A A. A. Zaitov
%T Geometrical and topological properties of a subspace $P_f(X)$ of probability measures
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 28-37
%N 10
%U http://geodesic.mathdoc.fr/item/IVM_2019_10_a3/
%G ru
%F IVM_2019_10_a3
A. A. Zaitov. Geometrical and topological properties of a subspace $P_f(X)$ of probability measures. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 28-37. http://geodesic.mathdoc.fr/item/IVM_2019_10_a3/

[1] Schepin E. V., “Funktory i neschetnye stepeni kompaktov”, UMN, 36:3 (1981), 3–62

[2] Fedorchuk V. V., Filippov V. V., Obschaya topologiya. Osnovnye konstruktsii, Fizmatlit, M., 2006

[3] Zhuraev T. F., “Prostranstvo vsekh veroyatnostnykh mer s konechnymi nositelyami gomeomorfno beskonechnomernomu lineinomu prostranstvu”, Obschaya topologiya. Prostranstva i otobrazheniya, MGU, M., 1989, 66–70

[4] Zhuraev T. F., “Nekotorye osnovnye svoistva funktora $P_f$”, Vestn. MGU. Ser. matem.-mekhan., 1989, no. 6, 29–33

[5] Zhuraev T. F., “O funktore $P$ veroyatnostnykh mer”, Vestn. MGU. Ser. matem.-mekhan., 1990, no. 1, 26–30

[6] Zhuraev T. F., Nekotorye geometricheskie svoistva podfunktorov funktora $P$ veroyatnostnykh mer, No 4471-V89, VINITI AN SSSR, M.; MGU

[7] Borsuk K., Teoriya retraktov, Mir, M., 1971

[8] Borsuk K., Teoriya sheipov, Mir, M., 1976

[9] Varadarain V. S., “Mery na topologicheskikh prostranstvakh”, Matem. sb., 55(97) (1961)

[10] Chepmen T., Lektsii o $Q$-mnogoobraziyakh, Mir, M., 1981