Cut points in abcohesive, aposyndetic, and semi-locally connected spaces (Q1608225)

Summary: In 1941, F. B. Jones introduced aposyndesis, which generalizes the concept of semi-local connectedness defined earlier by \textit{G. T. Whyburn} [Analytic topology (1942), see Zbl 0036.12402, Zbl 0117.15804], in the study of continuum theory. Using Jones's idea, \textit{D. A. John} [\(A\)-sets and abcohesive spaces, Missouri J. Math. Sci. 5, No. 2, 63-67 (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 \textit{B. Lehman} [Can. J. Math. 28, No. 5, 1032-1050 (1976; Zbl 0343.54027)] and Whyburn (1942, 1968) are generalized; sufficient conditions for the existence of two nodal sets are established as well.