Geodesic
Functor of idempotent probability measures with compact support and open mappings
Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 693-706.

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

In this paper, we show that the functor of idempotent probability measures with compact support acting in the category of Tikhonov spaces and their continuous mappings is normal. It is found that this functor is monodic. Further, it is proved that the functor of idempotent probability measures with compact support preserves the openness of continuous mappings of Tikhonov spaces. 
@article{CMFD_2021_67_4_a5,
     author = {A. Ya. Ishmetov},
     title = {Functor of idempotent probability measures with compact support and open mappings},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {693--706},
     publisher = {mathdoc},
     volume = {67},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a5/}
}
TY  - JOUR
AU  - A. Ya. Ishmetov
TI  - Functor of idempotent probability measures with compact support and open mappings
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2021
SP  - 693
EP  - 706
VL  - 67
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a5/
LA  - ru
ID  - CMFD_2021_67_4_a5
ER  - 
%0 Journal Article
%A A. Ya. Ishmetov
%T Functor of idempotent probability measures with compact support and open mappings
%J Contemporary Mathematics. Fundamental Directions
%D 2021
%P 693-706
%V 67
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a5/
%G ru
%F CMFD_2021_67_4_a5
A. Ya. Ishmetov. Functor of idempotent probability measures with compact support and open mappings. Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 693-706. http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a5/

[1] Al-Kassas Yu., Metrizuemost i parakompaktnost prostranstv veroyatnostnykh mer, Diss. k.f.-m.n., MGU, M., 1991

[2] Zaitov A. A., “O prodolzhenii slabo additivnykh funktsionalov”, Dokl. AN RUz., 2005, no. 5, 3–7

[3] Zaitov A. A., “Teorema ob otkrytom otobrazhenii prostranstv slabo additivnykh odnorodnykh funktsionalov”, Mat. zametki, 88:5 (2010), 683–688 | MR | Zbl

[4] Zaitov A. A., “Geometricheskie i topologicheskie svoistva podprostranstva $P_{f}(X)$ veroyatnostnykh mer”, Izv. vuzov. Ser. mat., 2019, no. 10, 28–37 | Zbl

[5] Zaitov A. A., Ishmetov A. Ya., “O monade, porozhdennoi funktorom $I_{\beta}$”, Vestn. NUUz., 2013, no. 2, 61–64

[6] Zaitov A. A., Ishmetov A. Ya., “Gomotopicheskie svoistva prostranstva $I_{f}(X)$ idempotentnykh veroyatnostnykh mer”, Mat. zametki, 106:4 (2019), 531–542 | Zbl

[7] Zaitov A. A., Tozhiev I. I., “Funktsionalnye predstavleniya zamknutykh podmnozhestv kompakta”, Uzb. mat. zh., 2010, no. 1, 53–63 | MR

[8] Zaitov A. A., Kholturaev Kh. F., “O vzaimosvyazi funktorov $P$ veroyatnostnykh mer i $I$ idempotentnykh veroyatnostnykh mer”, Uzb. mat. zh., 2014, no. 4, 36–45 | MR

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

[10] Ishmetov A. Ya., “O funktore idempotentnykh veroyatnostnykh mer s kompaktnymi nositelyami”, Uzb. mat. zh., 2010, no. 1, 72–80 | MR

[11] Kolokoltsov V. N., “Idempotentnye struktury v optimizatsii”, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril., 65, 1999, 118–174 | Zbl

[12] Kolokoltsov V. N., Maslov V. P., “Idempotentnyi analiz kak apparat teorii upravleniya. I”, Funkts. analiz i ego prilozh., 23:1 (1989), 1–14 | MR

[13] Kolokoltsov V. N., Maslov V. P., “Idempotentnyi analiz kak apparat teorii upravleniya i optimalnogo sinteza. II”, Funkts. analiz i ego prilozh., 23:4 (1989), 53–62 | MR | Zbl

[14] Litvinov G. L., Maslov V. P., Shpiz G. B., “Idempotentnyi funktsionalnyi analiz. Algebraicheskii podkhod”, Mat. zametki, 69:5 (2001), 758–797 | MR | Zbl

[15] Maslov V. P., Kolokoltsov V. N., Idempotentnyi analiz i ego primenenie v optimalnom upravlenii, Fizmatlit, M., 1994

[16] Taimanov A. D., “O zamknutykh otobrazheniyakh”, Mat. sb., 46 (1955), 349–352

[17] Fedorchuk V. V., “Mnogoznachnye retraktsii i kharakterizatsiya $n$-myagkikh otobrazhenii”, Tr. Mosk. mat. ob-va, 51, 1988, 169–207 | Zbl

[18] Fedorchuk V. V., “Veroyatnostnye mery v topologii”, Usp. mat. nauk, 46:1 (1991), 41–80 | MR | Zbl

[19] Fedorchuk V. V., Sadovnichii Yu. V., “O nekotorykh topologicheskikh i kategornykh svoistvakh znakoperemennykh mer”, Fundam. i prikl. mat., 5:2 (1999), 597–618 | MR | Zbl

[20] Fedorchuk V. V., Filippov V. V., Obschaya topologiya. Osnovnye konstruktsii, MGU, M., 1988

[21] Chigogidze A. Ch., “O prodolzhenii normalnykh funktorov”, Vestn. Mosk. un-ta. Ser. 1. Mat. Mekh., 1984, no. 6, 23–26 | Zbl

[22] Schepin E. V., “Funktory i neschetnye stepeni kompaktov”, Usp. mat. nauk, 36:3 (1981), 3–62 | MR | Zbl

[23] Aubin J. P., Dynamic economic theory: A viability approach, Springer-Verlag, Berlin—Heidelberg, 1997 | Zbl

[24] Eilenberg S., Moore J., “Adjoint functors and triples”, Ill. J. Math., 9:3 (1965), 381–398 | Zbl

[25] Radul T. N., “On the functor of order-preserving functionals”, Comment. Math. Univ. Carolin., 39:3 (1998), 609–615 | MR | Zbl

[26] Radul T., Idempotent measures: absolute retracts and soft maps, 2018, arXiv: 1810.09140v1 [math.GN]

[27] Zaitov A. A., “Order-preserving variants of the basic principles of functional analysis”, Fundame. J. Math. Appl., 2:1 (2019), 10–17

[28] Zaitov A. A., “On a metric on the space of idempotent probability measures”, Appl. Gen. Topol., 21:1 (2020), 35–51 | DOI | MR | Zbl