Multiplicity of a space over another space

• Taniyama Kouki

  Department of Mathematics, School of Education, Waseda University

抄録

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.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

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

  一般社団法人 日本数学会

キーワード

• multiplicity
• category
• topological space
• group
• module
• knot

詳細情報

• CRID: 1390282680092901120
• NII論文ID: 10031177251
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06430823
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 023829391
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I023829391
• 本文言語コード: en
• データソース種別:
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• 抄録ライセンスフラグ: 使用不可