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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 12, Pages 717-725

Cut points in abcohesive, aposyndetic, and semi-locally connected spaces

1Missouri Western State College, Saint Joseph, MO 64507, USA
2Central Missouri State University, Warrensburg, MO 64093, USA

Received 17 September 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In 1941, F. B. Jones introduced aposyndesis, which generalizes the concept of semi-local connectedness defined earlier by G. T. Whyburn (1942), in the study of continuum theory. Using Jones's idea, D. A. John (1993) defined abcohesiveness as a generalization of aposyndesis and studied the A-sets in abcohesive spaces. In this paper, some properties of abcohesive spaces are studied and a number of results by B. Lehman (1976) and Whyburn (1942, 1968) are generalized; sufficient conditions for the existence of two nodal sets are established as well.