Characterization of the Finite Partition Property for a Collection of Universal Subcontinua
نویسنده
چکیده
Let X be a Hausdorff space and A EX a continuum. A is said to be a Universal Subcontinuum (USC) if AH\B is connected for every continuum B EX. Let a be a collection of USC's of a Hausdorff space. Then a is said to have the finite partition property if a has a decomposition into a finite number of subcollections each having the finite intersection property. A result due to W. J. Gray [l] can be easily modified to show that in a Hausdorff space, a collection of USC's has the finite intersection property if every pair has a common point. Other properties of USC's are given in [2] and [3].
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