We study general-topological and infinite-dimensional properties of the Fell topology on the hyperspace $\mathrm{Cld}^*_F(X)$ of closed subsets of a locally compact paracompact space $X$.

1. Arkhangelski A.V. Structure and classification of topological spaces and cardinal invariants, Uspekhi Mat. Nauk, 33 (1978), no 6, 29--64 (in Russian).

2. Banakh T. The strongly universal property in convex sets, Matem. Studii, 10 (1998), 203--218.

3. Bell M. On character and chain conditions in images of products, Fundam. Math. 158 (1998), no. 1, 41--49.

4. Beer G. Topologies on Closed and Closed Convex Sets, Kluwer Academic, Dordrecht, 1993.

5. Banakh T., Radul T., Zarichnyi M. Absorbing Sets in Infinite-Dimensional Manifolds, VNTL Publishers, Lviv, 1996.

6. Curtis D., Nguyen To Nhu Hyperspaces of finite subsets which are homeomorphic to $\aleph_0$-dimensional linear metric spaces, Topol. Appl. 19 (1985), 251--260.

7. Costantini C., Kubiś W. Paths in hyperspaces, Appl. Gen. Topol. 4 (2003), 377--390.

8. Comfort W. Topological groups // in: Handbook of set-theoretic topology (K. Kunen, T.E. Vaughan eds.), Elsevier Sci. Publ., 1984, 1143--1263.

9. Curtis D.W., Schori R.M. Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), 19--38.

10. Curtis D.W. Hyperspaces of non-compact metric spaces, Comp. Math. 40 (1980), 139--152.

11. Curtis D.W. Boundary sets in the Hilbert cube, Topol Appl. 20 (1985), 201--221.

12. Curtis D.W. Hyperspaces of finite subsets as boundary sets, Topol Appl. 22 (1986), 97--107.

13. Engelking R. General Topology. PWN, Warszawa, 1977.

14. Fell J.M.G. A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472--476.

15. Fedorchuk V.V., Filippov V.V. General topology. Basic constructions, Moscow Univ. Press, Moscow. (in Russian).

16. Fedorchuk V., Todor cevi c S. Cellularity of covariant functors, Topology Appl. 76 (1997), no. 2, 125--150.

17. Glushkov V.M. Structure of locally compact topological groups and the Hilbert's Fifth Problem, Uspekhi Mat. Nauk, 74 (1957), no. 2, 2--41 (in Russian).

18. Hou, Ji-Cheng Character and tightness of hyperspaces with the Fell topology, Topology Appl. 84 (1998), 199--206.

19. Illanes A., Nadler S. Hyperspaces: fundamentals and recent advances, PAM 216. NY: Marcel Dekker, 1999.

20. Kelley J.L., General topology, Nauka, Moscow, 1968 (in Russian).

21. Leiderman A., Protasov I. Cellularity of the spaces of subgroups of discrete groups, manuscript.

22. Shapiro L. Spaces of closed subsets of bicompacta, Soviet Math. Dokl. 17 (1976), no. 3, 937–-941.

23. Sakai K., Wong R.Y. On infinite-dimensional manifold triples, Trans. Amer. Math. Soc. 318 (1990), 545--555.

24. Sakai K., Yang Z. Hyperspaces of non-compact metrizable spaces which are homeomorphic to the Hilbert cube, Topology Appl. 127 (2003), 331--342.

25. Teleiko A., Zarichnyi M. Categorial topology of compact Hausdorff spaces, VNTL Publishers, Lviv, 1999.

26. Todor cevi c S. Topics in topology, Springer-Verlag, 1997.


Author	T. O. Banakh, R. I. Voytsitskyy tbanakh@yahoo.com, voytsitski@mail.lviv.ua Faculty of Mechanics and Mathematics, Lviv Ivan Franko National University,
Abstract	We study general-topological and infinite-dimensional properties of the Fell topology on the hyperspace $\mathrm{Cld}^*_F(X)$ of closed subsets of a locally compact paracompact space $X$.
Keywords	Fell topology, hyperspace, locally compact paracompact space
DOI	doi:10.30970/ms.27.2.196-207
Reference	1. Arkhangelski A.V. Structure and classification of topological spaces and cardinal invariants, Uspekhi Mat. Nauk, 33 (1978), no 6, 29--64 (in Russian). 2. Banakh T. The strongly universal property in convex sets, Matem. Studii, 10 (1998), 203--218. 3. Bell M. On character and chain conditions in images of products, Fundam. Math. 158 (1998), no. 1, 41--49. 4. Beer G. Topologies on Closed and Closed Convex Sets, Kluwer Academic, Dordrecht, 1993. 5. Banakh T., Radul T., Zarichnyi M. Absorbing Sets in Infinite-Dimensional Manifolds, VNTL Publishers, Lviv, 1996. 6. Curtis D., Nguyen To Nhu Hyperspaces of finite subsets which are homeomorphic to $\aleph_0$-dimensional linear metric spaces, Topol. Appl. 19 (1985), 251--260. 7. Costantini C., Kubiś W. Paths in hyperspaces, Appl. Gen. Topol. 4 (2003), 377--390. 8. Comfort W. Topological groups // in: Handbook of set-theoretic topology (K. Kunen, T.E. Vaughan eds.), Elsevier Sci. Publ., 1984, 1143--1263. 9. Curtis D.W., Schori R.M. Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), 19--38. 10. Curtis D.W. Hyperspaces of non-compact metric spaces, Comp. Math. 40 (1980), 139--152. 11. Curtis D.W. Boundary sets in the Hilbert cube, Topol Appl. 20 (1985), 201--221. 12. Curtis D.W. Hyperspaces of finite subsets as boundary sets, Topol Appl. 22 (1986), 97--107. 13. Engelking R. General Topology. PWN, Warszawa, 1977. 14. Fell J.M.G. A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472--476. 15. Fedorchuk V.V., Filippov V.V. General topology. Basic constructions, Moscow Univ. Press, Moscow. (in Russian). 16. Fedorchuk V., Todor cevi c S. Cellularity of covariant functors, Topology Appl. 76 (1997), no. 2, 125--150. 17. Glushkov V.M. Structure of locally compact topological groups and the Hilbert's Fifth Problem, Uspekhi Mat. Nauk, 74 (1957), no. 2, 2--41 (in Russian). 18. Hou, Ji-Cheng Character and tightness of hyperspaces with the Fell topology, Topology Appl. 84 (1998), 199--206. 19. Illanes A., Nadler S. Hyperspaces: fundamentals and recent advances, PAM 216. NY: Marcel Dekker, 1999. 20. Kelley J.L., General topology, Nauka, Moscow, 1968 (in Russian). 21. Leiderman A., Protasov I. Cellularity of the spaces of subgroups of discrete groups, manuscript. 22. Shapiro L. Spaces of closed subsets of bicompacta, Soviet Math. Dokl. 17 (1976), no. 3, 937–-941. 23. Sakai K., Wong R.Y. On infinite-dimensional manifold triples, Trans. Amer. Math. Soc. 318 (1990), 545--555. 24. Sakai K., Yang Z. Hyperspaces of non-compact metrizable spaces which are homeomorphic to the Hilbert cube, Topology Appl. 127 (2003), 331--342. 25. Teleiko A., Zarichnyi M. Categorial topology of compact Hausdorff spaces, VNTL Publishers, Lviv, 1999. 26. Todor cevi c S. Topics in topology, Springer-Verlag, 1997.
Pages	196-207
Volume	27
Issue	2
Year	2007
Journal	Matematychni Studii
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