Geodesic
Topological properties of the space of $G$-symmetric degree
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 78-87.

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In this paper, we examine the weight, character, locally weak density, and metrizability of the space of $G$-symmetric degree. We proved that the mapping $\pi_{n,G}^{s}$ is open-closed, and the functor $SP_{G}^{n}$ preserves weight, net weight, character, local weak density, the Hausdorff property, regularity, completely regularity, metrizability, and connectedness.
Keywords: open-closed mapping, metrizability, weight, weak density, connectedness, character. 
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R. B. Beshimov; R. M. Juraev. Topological properties of the space of $G$-symmetric degree. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 78-87. http://geodesic.mathdoc.fr/item/INTO_2021_197_a8/

[1] Beshimov R. B., “O slaboi plotnosti nepreryvnykh otobrazhenii”, Uzbek. mat. zh., 1 (2001), 3–8 | MR

[2] Zarichnyi M. M., “Kharakterizatsiya funktorov $G$-simmetricheskoi stepeni i prodolzheniya funktorov na kategorii Kleisli”, Mat. zametki., 52:5 (1992), 42–48 | MR | Zbl

[3] Fedorchuk V. V., “Kovariantnye funktory v kategorii kompaktov, absolyutnye retrakty i $Q$-mnogoobraziya”, Usp. mat. nauk., 3 (36) (1981), 177–195 | Zbl

[4] Fedorchuk V. V., Filippov V. V., Topologiya giperprostranstv i ee prilozheniya, Znanie, M., 1989

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

[6] Engelking R., Obschaya topologiya, Mir, M., 1986

[7] Beshimov R. B., “Some cardinal properties of topological space connected with weakly density”, Meth. Funct. Anal. Topol., 10:3 (2004), 17–22 | MR | Zbl

[8] Beshimov R. B., “On some cardinal invariants of hyperspaces”, Mat. Stud., 24:2 (2005), 197–202 | MR | Zbl

[9] Beshimov R. B., Mukhamadiev F. G. and Mamadaliev N. K., “The local density and the local weak density of hyperspaces”, Int. J. Geom., 4:1 (2015), 42–49 | Zbl

[10] Beshimov R. B., Safarova D. T., “Normal functors and two P. S. Aleksandrov's arrows”, Caspian J. Appl. Math., 1:2 (2013), 50–59

[11] Beshimov R. B., Zhuraev R. M., “Separation axioms of space of the permutation degree”, Tr. Mezhdunar. konf. «Sovremennye problemy geometrii i topologii i ikh prilozheniya» (Tashkent, 21–23 noyabrya 2019 g.), Tashkent, 2019, 30–31

[12] Michael E., “Topologies on spaces of subsets”, Trans. Am. Math. Soc., 71 (1951), 152–182 | DOI | Zbl

[13] Mukhamadiev F., “Some cardinal and topological properties of the $n$-permutation degree of a topological spaces and locally $\tau$-density of hyperspaces”, Bull. Natl. Univ. Uzbekistan. Math. Nat. Sci., 1:1 (2018), 3–25 | MR