Multiplicity of a space over another space

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another. Based on this multiplicity, we define a pseudo distance on the class of objects. We define and study several multiplicities in the category of topological spaces and continuous maps, the category of groups and homomorphisms, the category of finitely generated R-modules and R-linear maps over a principal ideal domain R, and the neighbourhood category of oriented knots in the 3-sphere.

    Original languageEnglish
    Pages (from-to)823-849
    Number of pages27
    JournalJournal of the Mathematical Society of Japan
    Volume64
    Issue number3
    DOIs
    Publication statusPublished - 2012

    Fingerprint

    Multiplicity
    Principal ideal domain
    Linear map
    Continuous Map
    Morphism
    Morphisms
    Homomorphisms
    Topological space
    Finitely Generated
    Knot
    Module
    Object

    Keywords

    • Category
    • Group
    • Knot
    • Module
    • Multiplicity
    • Topological space

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Multiplicity of a space over another space. / Taniyama, Kouki.

    In: Journal of the Mathematical Society of Japan, Vol. 64, No. 3, 2012, p. 823-849.

    Research output: Contribution to journalArticle

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