Vol. 37, No. 3, 1971

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Aposyndetic properties of unicoherent continua

Donald Earl Bennett

Vol. 37 (1971), No. 3, 585–589

In the first part of this paper the structure of n-aposyndetic continua is studied. In particular, those continua which are n-aposyndetic but fail to be (n + 1)-aposyndetic are investigated. Unicoherence is shown to be a sufficient condition for an n-aposyndetic continuum to be (n + 1)-aposyndetic. In the final portion of the paper a stronger form of unicoherence is defined. As a point-wise property, aposyndesis and connected im kleinen are shown to be equivalent in continua with this property.

Mathematical Subject Classification 2000
Primary: 54F15
Received: 21 September 1970
Published: 1 June 1971
Donald Earl Bennett