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Proceedings of the American Mathematical Society

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On the first countability of hyperspaces

Author: Takemi Mizokami
Journal: Proc. Amer. Math. Soc. 67 (1977), 152-156
MSC: Primary 54B20
MathSciNet review: 0454899
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Abstract: In this paper, the heredity of first countability of a space X on the hyperspace $ \mathcal{C}(X)$ of nonempty compact subsets of X with the finite topology is investigated and some variations are given.

References [Enhancements On Off] (What's this?)

  • [1] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. MR 0042109 (13:54f)
  • [2] E. Michael and K. Nagami, Compact-covering images of metric spaces, Proc. Amer. Math. Soc. 37 (1973), 260-266. MR 0307148 (46:6269)
  • [3] V. Ponomarev, Axioms of countability and continuous mappings, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1968), 127-134. MR 0116314 (22:7109)
  • [4] R. E. Smithson, First countable hyperspaces, Proc. Amer. Math. Soc. 56 (1976), 325-328. MR 0402667 (53:6483)
  • [5] H. H. Wiche, On the Hausdorff open continuous images of Hausdorff paracompact p-spaces, Proc. Amer. Math. Soc. 22 (1969), 136-140. MR 0243480 (39:4801)

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Keywords: Hyperspaces, the finite topology, countable character, open and compact-covering mappings
Article copyright: © Copyright 1977 American Mathematical Society

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