Vol. 45, No. 2, 1973

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Non-aposyndesis and non-hereditary decomposability

Harold Eugene Schlais

Vol. 45 (1973), No. 2, 643–652

Let M be a compact metric continuum. If x M let K(x) be the set to which an element y of M belongs if and only if M is not aposyndetic at x wilh respect to y. If, for all x in M,x Int(K(x)), then M is the union of a countable collection of indecomposable subcontinua each of which is the closure of an open set. There exists a compact metric continuum M and a dense subset J of M such that for each x J,K(x) = S, but M contains no indecomposable subcontinua with nonvoid interior. It is the case, however, that if M has a point x such that Int (K(x)) = lhen M contains an indecomposable subcontinua which intersects Int (K(x)).

Mathematical Subject Classification 2000
Primary: 54F15
Received: 1 December 1971
Published: 1 April 1973
Harold Eugene Schlais