Geodesic
Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures
Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 531-542.

Voir la notice de l'article provenant de la source Math-Net.Ru

A subspace $I_f(X)$ of the space of idempotent probability measures on a given compact space $X$ is constructed. It is proved that if the initial compact space $X$ is contractible, then $I_f(X)$ is a contractible compact space as well. It is shown that the shapes of the compact spaces $X$ and $I_f(X)$ are equal. It is also proved that, given a compact space $X$, the compact space $I_f(X)$ is an absolute neighborhood retract if and only if so is $X$.
Keywords: idempotent measure, compact space, absolute neighborhood retract, shape. 
@article{MZM_2019_106_4_a4,
     author = {A. A. Zaitov and A. Ya. Ishmetov},
     title = {Homotopy {Properties} of the {Space} $I_f(X)$ of {Idempotent} {Probability} {Measures}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {531--542},
     publisher = {mathdoc},
     volume = {106},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a4/}
}
TY  - JOUR
AU  - A. A. Zaitov
AU  - A. Ya. Ishmetov
TI  - Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures
JO  - Matematičeskie zametki
PY  - 2019
SP  - 531
EP  - 542
VL  - 106
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a4/
LA  - ru
ID  - MZM_2019_106_4_a4
ER  - 
%0 Journal Article
%A A. A. Zaitov
%A A. Ya. Ishmetov
%T Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures
%J Matematičeskie zametki
%D 2019
%P 531-542
%V 106
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a4/
%G ru
%F MZM_2019_106_4_a4
A. A. Zaitov; A. Ya. Ishmetov. Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures. Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 531-542. http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a4/

[1] V. P. Maslov, V. N. Kolokoltsov, Idempotentnyi analiz i ego primenenie v optimalnom upravlenii, Nauka, M., 1994 | MR

[2] Idempotent Mathematics and Mathematical Physics, Contemp. Math., 377, eds. G. L. Litvinov, V. P. Maslov, Amer. Math. Soc., Providence, RI, 2005 | MR | Zbl

[3] G. L. Litvinov, “Dekvantovanie Maslova, idempotentnaya i tropicheskaya matematika: kratkoe vvedenie”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye i algoritmicheskie metody. XIII, Zap. nauchn. sem. POMI, 326, POMI, SPb., 2005, 145–182 | MR | Zbl

[4] P. Bernhard, “Max-plus algebra and mathematical fear in dynamic optimization”, Set-Valued Anal., 8:1-2 (2000), 71–84 | DOI | MR | Zbl

[5] J. P. Aubin, O. Dordan, “Fuzzy systems, viability theory and toll sets”, Fuzzy Systems, Handb. Fuzzy Sets Ser., 2, Kluwer Acad. Publ., Boston, MA, 1998, 461-488 | MR | Zbl

[6] J.-P. Aubin, Dynamic Economic Theory. A Viability Approach, Stud. Econom. Theory, 5, Springer-Verlag, Berlin, 1997 | MR | Zbl

[7] V. V. Fedorchuk, “Veroyatnostnye mery v topologii”, UMN, 46:1 (277) (1991), 41–80 | MR | Zbl

[8] M. M. Zarichnyi, “Prostranstva i otobrazheniya idempotentnykh mer”, Izv. RAN. Ser. matem., 74:3 (2010), 45–64 | DOI | MR | Zbl

[9] E. V. Schepin, “Funktory i neschetnye stepeni kompaktov”, UMN, 36:3 (219) (1981), 3–62 | MR | Zbl

[10] V. V. Fedorchuk, “Vpolne zamknutye otobrazheniya i ikh prilozheniya”, Fundament. i prikl. matem., 9:4 (2003), 105–235 | MR | Zbl

[11] A. A. Zaitov, Geometrical Properties of the Space $P_f (X)$ of Probability Measures, 2018, arXiv: 1809.03331

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

[13] K. Borsuk, Teoriya retraktov, Mir, M., 1971 | MR | Zbl

[14] T. Chepmen, Lektsii o $Q$-mnogoobraziyakh, Mir, M., 1981 | MR

[15] T. Radul, Idempotent Measures: Absolute Retracts and Soft Maps, 2018, arXiv: 1810.09140