Making holes in hyperspaces |
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Authors: | José G Anaya |
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Institution: | Instituto de Matemáticas, UNAM, Circuito Exterior, Cuidad Universitaria, 04510 México, D.F., Mexico |
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Abstract: | Let X be a metric continuum and C(X) the hyperspace of all nonempty subcontinua of X. Let A∈C(X), A is said to make a hole in C(X), if C(X)−{A} is not unicoherent. In this paper we study the following problem.Problem: For which A∈C(X), A makes a hole in C(X).In this paper we present some partial solutions to this problem in the following cases: (1) A is a free arc; (2) A is a one-point set; (3) A is a free simple closed curve; (4) A=X. |
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Keywords: | primary 54B20 secondary 54F55 |
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