•  
  •  
 

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

In this paper, we investigate the heredity of some kind of generalized metric spaces to ecX and enX. We will study the connection between a σ-space, Σ-space, a stratifiable space, ℵ-space, ℵ0-space and its hyperspace.

First Page

269

Last Page

277

References

1. Vietoris A. Bereiche Zweiter Ordnung. Monatsh, fur math, und phys, Issue 32, 258–280 (1922).

2. Michael E. Topologies on spaces of subsets. Trans. Amer. Math. Soc., Vol. 71, Issue 1, 152–172 (1951).

3. Fedorchuk V.V., Todorcevic S. Cellularity of Covariant functors. Topology and its applications, Vol. 76, Issue 1, 125–150 (1997).

4. Beshimov R.B. On some cardinal invariants of hyperspaces. Mathematychni Studii, Vol. 24, Issue 2, 197–202 (2005).

5. Beshimov R.B., Mamadaliev N.K. and Eshtemirova Sh.Kh. Categorical and cardinal properties of hyperspaces with a finite number of components. Journal of Mathematical Sciences, Vol. 245, Issue 3, 390–397 (2020).

6. Mizokami T. On hyperspaces of spaces around Moore spaces. Hauston Journal of Mathematics, Vol. 22, 297–306 (1996).

7. Mizokami T. On hyperspaces of generalized metric spaces. Topology and its applications, Vol. 76, 169–173 (1997).

8. Fedorchuk V.V. Covariant functors in the category of compacta absolute retracts and Q manifolds. UMN, Vol. 3, Issue 36, 177–195 (1981).

9. Beshimov R.B., Mamadaliev N.K. Categorical and topological properties of the functor of Radon functionals. Topology and its Applications, Vol. 275, 1–11 (2020).

10. Beshimov R.B., Zhuraev R.M. Some properties of a connected topological group. Mathematics and Statistics, Vol. 7, Issue 2, 45–49 (2019).

11. Fedorchuk V.V., Filippov V.V. General topology. Basic constructions. Moscow: Fizmatlit, 314 (2006).

12. Fedorchuk V.V. Infinite-dimensional bicompacta. Izvestia. USSR Academy of Sciences, ser. maths, Vol. 42, 1162–1178 (1978).

13. Ganea T. Symmetrische Potenzen Topologischer Raume. Math. Nach., Vol. 11, 305–316 (1954).

14. Engelking R. General topology. Revised and completed edition. Berlin. Helderman, 752 (1986).

15. Banakh T. Topological spaces with an ω-base. Dissertations Mathemeticae, Warszawa, (2019).

16. Nagata J. Modern General Topology. North-Holland Mathematical Library, 522 (1984).

17. Gruenhage G. Generalized metric spaces. Handbook of Set Theoretic Topology, 423–502 (1983).

18. Borges C.R. Normality of hyperspaces. Math. Japon, Vol. 25, 507–508 (1980).

19. Morita K. On the dimension of product spaces. Amer Journal of mathematics, Vol. 75, 205–223 (1953).

20. Nagami K. Σ-space. Fundamental Mathematic, Vol. 65, 169–192 (1969).

21. Borges C.R. On stratifiable spaces. Pacific Journal of Mathematics, Vol. 17, 1–16 (1966).

22. Lin F., Liu Ch. The k-spaces property of the free Abelian topological groups over non-metrizable Lasnev spaces. Topology and its Applications, Vol. 220, 31–42 (1917).

23. Beshimov R.B., Mamadaliyev N.K. and Mukhamadiyev F.G. π-Irreducible Mappings and k-network of Infinite Compacts. British Journal of Mathematics Computer Science, Vol. 10, Issue 5, 1–7 (2015).

24. Creede G.D. Concerning semi-stratifiable spaces. Pacific Journal of Mathematics, Vol. 32, Issue 1, 1–7 (1970).

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.