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The Antisymmetry Betweenness Axiom And Hausdorff Continua, Paul Bankston
The Antisymmetry Betweenness Axiom And Hausdorff Continua, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
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.