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An interpretation of betweenness on a set satisfies the antisymmetry axiom at a point a if it is impossible for each of two distinct points to lie between the other and a. In this paper we study the role of antisymmetry as it applies to the K-interpretation of betweenness in a Hausdorff continuum X, where a point c lies between points a and b exactly when every subcontinuum of X containing both a and b contains c as well.
Bankston, Paul, "The Antisymmetry Betweenness Axiom and Hausdorff Continua" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 223.