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Published in:
2013 | OriginalPaper | Chapter
New Structures Based on Completions
Author : Gilles Bertrand
Published in: Discrete Geometry for Computer Imagery
Publisher: Springer Berlin Heidelberg
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We propose new axioms relative to combinatorial topology. These axioms are settled in the framework of completions which are inductive properties expressed in a declarative way, and that may be combined.
We introduce several completions for describing
dyads
. A dyad is a pair of complexes which are, in a certain sense, linked by a “relative topology”.
We first give some basic properties of dyads, then we introduce a second set of axioms for
relative dendrites
. This allows us to establish a theorem which provides a link between dyads and dendrites, a dendrite is an acyclic complex which may be also described by completions. Thanks to a previous result, this result makes clear the relation between dyads, relative dendrites, and complexes which are acyclic in the sense of homology.