Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

LOCAL CONNECTEDNESS IN FELL TOPOLOGY

  • Hur, K. (Department of mathematics Won Kwang University) ;
  • Moon, J.R. (Department of mathematics Won kwang University) ;
  • Rhee, C.J. (Department of Mathematics Wayne State University)
  • Published : 1999.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let $C(X)(C_{K}(X))$ denote the hyperspace of all nonempty closed connected subsets (subcontinua) of a locally compact Haus-dorff space X with the Fell topology. We prove that the following statements are equivalent: (1) X is locally connected. (2) C(X) is locally connected,. (3) C(X) is locally connected at each $E{\in}C_{k}(X).(4) C_{k}(X)$ is locally connected.

Keywords

References

  1. Set-valued Analysis v.1 On the Fell topology Beer, G.
  2. Proc. Amer. Math. Soc. v.13 A Hausdorff topology for the closed subsets of locally compact non-Hausdorff space Fell, J. M. G.
  3. Pacif. J. Math. v.53 Connectedness im kleinen and local connectedness in$2^Xx$and C(X) Goodykoontz, Jack T., Jr.
  4. Proc. Amer. Math. Soc. v.65 More on connectedness im kleinen and local connectedness in C(X) Goodykoontz, Jack T., Jr.
  5. Hoston J. Math. v.4 Local arcwise connectedness in$2^X$and C(X) Goodykoontz, Jack T., Jr.
  6. Theory of correspondences Klein, E.;Thomas, A.
  7. Canadian Math. J. v.20 Arcs, semigroups, and hyperspaces McWater, M. M.
  8. Trans. Amer. Math. Soc. v.71 Topologies on spaces of subsets Michael, E.
  9. Hyperspaces of sets Nadler, Sam B., Jr.
  10. Fund. Math. v.59 Einig Bemerkungen uber den Raum der abgesschossenen Mengen Poppe, Harry
  11. Local properties of hyperspaces Rhee, C. J.
  12. Soviet Math. Dokl. v.15 On the connectedness of hyperspaces Tasmetov, U.
  13. Fund. Math. v.32 Retractes absolus et hyperspaces des continus Wojdslawski, M.