Open Access
July, 2012 Multiplicity of a space over another space
J. Math. Soc. Japan 64(3): 823-849 (July, 2012). DOI: 10.2969/jmsj/06430823


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.


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Kouki TANIYAMA. "Multiplicity of a space over another space." J. Math. Soc. Japan 64 (3) 823 - 849, July, 2012.


Published: July, 2012
First available in Project Euclid: 24 July 2012

zbMATH: 1276.18010
MathSciNet: MR2965429
Digital Object Identifier: 10.2969/jmsj/06430823

Primary: 18D99
Secondary: 13C05 , 20E99 , 57M25 , 57M99

Keywords: category , group , knot , module , multiplicity , topological space

Rights: Copyright © 2012 Mathematical Society of Japan

Vol.64 • No. 3 • July, 2012
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