Arcwise connectedness of the complement in a hyperspace

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概要

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• The hyperspace C(X) of a continuum X is always arcwise connected. In [6], S.B.Nadler Jr. and J.Quinn show that of C(X)-{Ai} is arcwise connected for each i=1,2, then C(X)-{A1.A2} is alsp arcwise connected. Nadler raised questions in his book [5]: Is it ture with the two sets A1 and A2 replaced by n sets, n finite? What about comtably many? What about a collection {Aλ:λ∈A} which is a compact zero-dimensional subset of the hyperspace? in this paper we porve that if A⊂C(X) is a closed countable subset, U is an arc component of an open set of C(X) and C(X)-{a} is arcwise connected for each A∈A, then U-A is arcwise connected.

• 筑波大学の論文
• 1997-01-10

著者

• Hiroshi Hosokawa

  Institute Of Mathematics University Of Tsukuba

• Hosokawa Hiroshi

  Institute of Mathematics University of Tsukuba

関連論文

• Induced mappings on hyperspaces II
• Arcwise connectedness of the complement in a hyperspace
• Induced mappings on hyperspaces

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