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Item type:Publication, Access status: with files , Topics in abstract order geometryAn interval space is a set with a ternary relation satisfying some axioms that support the interpretation of the ternary relation as location of a point between two points. Some new concepts, including those of a topological, a quadrimodular and a quadrimedian interval space and a geodesic quadrimedian closure are developed. A sufficient criterion for embeddability of an interval space into a median metric space is proved. For two central structure theorems of analysis and algebra it is proved that analogues are valid for quadrimedian spaces, but do not hold in general for median spaces.Publicationtype: Doctoral Thesis424 1061