Glasnik Matematicki, Vol. 47, No. 1 (2012), 187-192.

CONCERNING N-MUTUAL APOSYNDESIS IN HYPERSPACES

Alejandro Illanes

Abstract.   Given a metric continuum X, let 2^X denote the hyperspace of nonempty closed subsets of X. We prove that 2^X is n-mutually aposyndetic for each n≥ 1. That is, given n distinct elements of 2^X, there are n disjoint subcontinua of 2^X, each containing one of the elements in its interior.

2010 Mathematics Subject Classification.   54B20, 54F15.

Key words and phrases.   Continuum, hyperspace, n-mutual aposyndesis.

DOI: 10.3336/gm.47.1.17

References:

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2. H. Hosokawa, Mutual aposyndesis of n-fold hyperspaces, Houston J. Math. 35 (2009), 131-137.
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