SOME HOMOTOPY PROPERTIES OF n-FOLD SYMMETRIC PRODUCT OF THE SPACE X
In this paper, we study some homotopy properties of the space n-fold symmetric product of the
space X. We prove that if mappings f; g : X ! Y are homotopic, then the mappings Fnf;Fng :
FnX ! FnY are also homotopic. Also shown that the functor of n-fold symmetric product Fn is a
covariant homotopy functor. Besides proved that if spaces X and Y are homotopically equivalent,
then the spaces FnX and FnY are also homotopically equivalent.
1. Beshimov R. B., Safarova D. T. Some Topological Properties of a Functor of Finite Degree. Lobachevskii
of Journal Mathematics, 2021, V.42, P.2744–2753.
2. Beshimov R. B., Safarova D. T. Uniformly linked space and its hyperspace. AIP Conference Proceedings,
2024, V.3004(1), P.020003.
3. Koˇcinac Lj. D. R., Mukhamadiev F. G., Sadullaev A. K. On some properties of the superextension functor.
Herald of Institute Mathematics of the National Academy of Sciences of the Kyrgyz Republic, 2022, V.2,
P.5–18.
4. Koˇcinac Lj. D. R., Mukhamadiev F. G., Sadullaev A. K. On the superextension functor. AIP Conference
Proceedings, 2023, V.2879(1), P.020004.
5. Koˇcinac Lj. D. R., Mukhamadiev F. G., Sadullaev A. K. Some Cardinal and Geometric Properties of the
Space of Permutation Degree. Axioms, 2022, V.11(6), P.290.
6. Mukhamadiev F. G. Some homotopy properties of the space of complete linked systems. Selected papers
of the 2023 International Conference on Topology and its Applications. In press.
7. Fedorchuk V. V., Filippov V. V. opology of Hyperspaces and Its Applications. Znanie: Moscow, Russia,
1989. (In Russian)
8. Shchepin E. V. Functors and uncountable powers of compacta. Math. Surveys. 1981, V.36:3, P.1–7.
9. Good C., Macias S. Symmetric products of generalized metric spaces. Topology Appl. 2016, V.206, P.93–
114.
10. Tuyen L. Q., Tuyen O. V., Koˇcinac Lj. D. R. The Vietoris hyperspace F(X) and certain generalized metric
properties. Hacettepe Journal of Mathematics and Statistics, 2024, V.53(2), P.356–366.
11. Tang Z., Lin S., Lin F. Symmetric products and closed finite-to-one mappings. Topology and its
Applications, 2018, V.234, P.6–45.
12. Peng L. X., Sun Y. A study on symmetric products of generalized metric spaces. Topology and its
Applications, 2017, V.231, P.411–429.
13. Tuyen L. Q., Tuyen O. V. A note on the hyperspace of finite subsets. Fasciculi Math. 2021, V.65, P.67–73.
14. Yuldashev T. K., Mukhamadiev F. G. The local density and the local weak density in the space of
permutation degree and in Hattori space. Ural Mathematical Journal, 2020, V.6(2), P.108–116.
15. Kosniowski C. A First Course in Algebraic Topology. Cambridge University Press, 1980.
16. Munkres J. Topology, Secomnd ed. Pearson Education Limited, Edinburgh, 2014.
Copyright (c) 2024 «ACTA NUUz»
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
.jpg)
1.png)
