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An interpretation of betweenness on a set is gap free if each two distinct points of the set have a third point between them. In this paper we are interested in gap free betweenness relations naturally induced by the topology of Hausdorff continua. In particular, we say c lies between a and b in the K-interpretation precisely when every subcontinuum that contains both a and b also contains c. We explore the connection between K-gap freeness and hereditary unicoherence.
Bankston, Paul, "When Hausdorff Continua Have No Gaps" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 188.
Accepted version. Published as part of the proceedings of the conference, Summer Conference on General Topology and its Applications, 2014: 177-188. Publisher link. © 2014 Topology Proceedings. Used with permission.