Multiplicity of a space over another space

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Author(s)

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 <i>R</i>-modules and <i>R</i>-linear maps over a principal ideal domain <i>R</i>, and the neighbourhood category of oriented knots in the 3-sphere.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 64(3), 823-849, 2012-07-01

    The Mathematical Society of Japan

References:  10

Codes

  • NII Article ID (NAID)
    10031177251
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    023829391
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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