Embedding Topological Median Algebras in Products of Dendrons | Zendy

Bandelt H.J. | Zendy; van de Vel M. | Zendy

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Embedding Topological Median Algebras in Products of Dendrons

Author(s) -

Bandelt H.J.,

van de Vel M.

Publication year - 1989

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/s3-58.3.439

Subject(s) - embedding , mathematics , convexity , operator (biology) , product (mathematics) , metric (unit) , graph , pure mathematics , combinatorics , computer science , chemistry , geometry , biochemistry , operations management , repressor , artificial intelligence , transcription factor , financial economics , economics , gene

Dendrons and their products admit a natural, continuous median operator. We prove that there exists a two‐dimensional metric continuum with a continuous median operator, for which there is no median‐preserving embedding in a product of finitely many dendrons. Our method involves ideas and results concerning graph colouring and abstract convexity. The main result answers a question in [16] negatively, and is sharply contrasting with a result of Stralka [15] on embeddings of compact lattices.

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