| [176902] |
| Title: Topics in Abstract Order Geometry. |
| Written by: Wolfram Retter |
| in: September (2013). |
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| Series: 20130927-phdthesis-retter.pdf |
| Address: Hamburg / Germany |
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| ISBN: 10.15480/882.1154 |
| how published: 13-55 Retter13 PhD |
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| School: Hamburg University of Technology |
| Institution: School of Electrical Engineering, Computer Science and Mathematics |
| Type: Ph.D. Thesis. |
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Note: AEG
Abstract: An 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.