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Topics in abstract order geometry
Citation Link: https://doi.org/10.15480/882.1154
Other Titles
Themen in abstrakter Anordnungsgeometrie
Publikationstyp
Doctoral Thesis
Date Issued
2014
Sprache
English
Author(s)
Advisor
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2013-09-27
Institut
TORE-DOI
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.
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.
Subjects
Anordnungsgeometrie
Intervallräume
order geometry
interval spaces
ordered geometry
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