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- W4386080968 abstract "The main aim of the paper is to study in greater detail absolutely homogeneous structures (that is, objects with the property that each partial isomorphism extends to a global automorphism), with special emphasis on metric spaces and (possibly infinite, full) graphs with edge-coloring. Besides, a general categorical approach to this concept is presented. The main achievement of the paper is the discovery of one-to-one correspondence between absolutely homogeneous objects and certain classes (that become sets when isomorphic objects are identified) of finite objects that satisfy a few quite general axioms (such as amalgamation and heredity). It is also introduced and discussed in detail the concept of products for graphs with edge-coloring (that produces an absolutely homogeneous graph provided all factors are so). Among the most significant results of the paper, it is worth mentioning a full classification (up to isometry) of all absolutely homogeneous ultrametric spaces as well as of all absolutely homogeneous graphs with edge-coloring in which all triangles are isosceles or in which all triangles are (precisely) tricolored." @default.
- W4386080968 created "2023-08-23" @default.
- W4386080968 creator A5011006691 @default.
- W4386080968 date "2023-08-19" @default.
- W4386080968 modified "2023-09-27" @default.
- W4386080968 title "Extensive approach to absolute homogeneity" @default.
- W4386080968 doi "https://doi.org/10.48550/arxiv.2308.09986" @default.
- W4386080968 hasPublicationYear "2023" @default.
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