Geometrical properties of the space of idempotent probability measures

• Kholturayev, Kholsaid Fayzullayevich ^[1]
  1. [1] Tashkent Institute of Irrigation and Agricultural Mechanization Engineers
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 399-415
• Idioma: inglés
• DOI: 10.4995/agt.2021.15101
• Enlaces
  • Texto completo
• Resumen

  • Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''. At first we establish for a compact metric space X the spaces P(X) of probability measures and I(X) idempotent probability measures are homeomorphic ("parallelism''). Then we construct an example which shows that the constructions P and I form distinguished functors from each other ("parallelism'' negation). Further for a compact Hausdorff space X we establish that the hereditary normality of I3(X)\ X implies the metrizability of X.

• Referencias bibliográficas
  • G. Choquet, Theory of capacities, Ann. Inst. Fourier 5 (1955), 131-295. https://doi.org/10.5802/aif.53
  • V. V. Fedorchuk, Fully closed mappings and their applications, Fundam. Prikl.Mat. 9, no. 4 (2003), 105-235. [J .Math. Sci. (New York) 136:5,...
  • V. V. Fedorchuk, On Katetov's theorem on the cube, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1989, no. 4, 93-96.
  • V. V. Fedorchuk and V. V. Filippov, General Topology. Basic Constructions (in Russian). - Moscow. Fizmatlit. - 2006.
  • R. Garner, Topological functors as total categories, Theory Appl. Categ. 29, no. 15 (2014), 406-422.
  • J. Gunawardena, Idempotency, Publ. of the Newton Institute, 11 (1998), Cambridge University Press, Cambridge, (Online publication date: May...
  • E. Hopf, The partial differential equation equation ut + uux = µuxx, Comm. Pure Appl. Math. 3 (1950), 201-230. https://doi.org/10.1002/cpa.3160030302
  • A. Ya. Ishmetov, On functor of idempotent probability measures with compact support, Uzbek. Mat. Zh. 2010, no. 1 (2010), 72-80.
  • M. Katetov, Complete normality of Cartesian products. Fund. Math. 35 (1948), 271-274. https://doi.org/10.4064/fm-35-1-271-274
  • V. N. Kolokoltsov, Idempotent structures in optimization, J. Math. Sci. (New York) 104, no. 1 (2001), 847-880. https://doi.org/10.1023/A:1009514904187
  • V. N. Kolokoltsov and V. P. Maslov, Idempotent analysis as a tool of control theory and optimal synthesis. 1, Funct. Anal. Appl. 23, no. 1...
  • V. N. Kolokoltsov and V. P. Maslov, Idempotent analysis as a tool of control theory and optimal synthesis. 2, Funct. Anal. Appl. 23, no. 4...
  • G. L. Litvinov and V. P. Maslov, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics 377 (2005), 370 pp. https://doi.org/10.1090/conm/377
  • G. L. Litvinov, V. P. Maslov and S. N. Sergeev (eds), Idempotent and tropical mathematics and problems of mathematical physics, 1 (2007),...
  • E. V. Shchepin, Functors and uncountable powers of compacta, Uspekhi Mat. Nauk 36, no. 3 (1981), 3-62. https://doi.org/10.1070/RM1981v036n03ABEH004247
  • A. A. Zaitov and A. Ya. Ishmetov, Homotopy properties of the space If (X) of idempotent probability measures, Math. Notes 106, no. 3-4 (2019),...
  • A. A. Zaitov, Geometrical and topological properties of a subspace Pf (X) of probability measures (Russian), Russ Math. 63, no. 10 (2019),...
  • A. A. Zaitov, On a metric on the space of idempotent probability measures, Applied General Topology 21, no. 1 (2020), 35-51. https://doi.org/10.4995/agt.2020.11865
  • A. A. Zaitov and A. Ya. Ishmetov, On monad generating by the functor Iβ (Russian), Vestnik of National University of Uzbekistan 2 (2013),...
  • A. A. Zaitov and Kh. F. Kholturaev, On interrelation of the functors P of probability measures and I of idempotent probability measures (Russian),...
  • M. M. Zarichnyi, Spaces and maps of idempotent measures, Izv. Math. 74, no. 3 (2010), 481-499. https://doi.org/10.1070/IM2010v074n03ABEH002495