Abstract
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.
This work has been partially supported by the “ANR-2010-BLAN-0205 KIDICO” project.
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Bertrand, G. (2013). New Structures Based on Completions. In: Gonzalez-Diaz, R., Jimenez, MJ., Medrano, B. (eds) Discrete Geometry for Computer Imagery. DGCI 2013. Lecture Notes in Computer Science, vol 7749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37067-0_8
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DOI: https://doi.org/10.1007/978-3-642-37067-0_8
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