Journal of the Mathematical Society of Japan

Multiplicity of a space over another space

Kouki TANIYAMA

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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.

Article information

Source
J. Math. Soc. Japan, Volume 64, Number 3 (2012), 823-849.

Dates
First available in Project Euclid: 24 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1343133745

Digital Object Identifier
doi:10.2969/jmsj/06430823

Mathematical Reviews number (MathSciNet)
MR2965429

Zentralblatt MATH identifier
1276.18010

Subjects
Primary: 18D99: None of the above, but in this section
Secondary: 13C05: Structure, classification theorems 20E99: None of the above, but in this section 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M99: None of the above, but in this section

Keywords
multiplicity category topological space group module knot

Citation

TANIYAMA, Kouki. Multiplicity of a space over another space. J. Math. Soc. Japan 64 (2012), no. 3, 823--849. doi:10.2969/jmsj/06430823. https://projecteuclid.org/euclid.jmsj/1343133745


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