Vol. 54, No. 2, 1974

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Monotone decompositions into trees of Hausdorff continua irreducible about a finite subset

Eldon Jon Vought

Vol. 54 (1974), No. 2, 253–261

This paper deals with characterizing two types cf monotone, upper semi-continuous decompositions of a Piausdoffi continuum that is irreducible about a finite subset. One of the decompositions is minimal with respect lo the property of having a quotient space which is a tree (a hereditarily unicoherent, locally connected continuum) and is characterized in terms of certain collections of subcontinua. The other decomposition is not only minimal but also unique with respect to the properties that the quotient space is a tree and the elements of the decomposition have void interiors. This decomposition is characterized quite simply by prohibiting the existence of indecomposable subcontinua with nonvoid interiors. The stmcture of the elements of Che decompositions that have void interiors is very nice and is described by means of the aposyndetic se5 function T. In the case where elements exist with nonvoid interiors, the stmcture can be very complicated and a final result deals with this structure under some rather stringent conditions.

Mathematical Subject Classification
Primary: 54F20
Received: 28 December 1972
Published: 1 October 1974
Eldon Jon Vought