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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.