このときに以下の二条件を満たす組 ( M , C ) {\displaystyle (M,C)} をいう[2]：

各々の H {\displaystyle H} につき H ∈ C ∞ ( R n ) {\displaystyle H\in C^{\infty }\left(\mathbb {R} ^{n}\right)} 。ここに n ∈ N {\displaystyle n\in \mathbb {N} } 、かつ任意の f 1 , … , f n ∈ C {\displaystyle f_{1},\dots ,f_{n}\in C} につき H ∘ ( f 1 , … , f n ) ∈ C {\displaystyle H\circ \left(f_{1},\dots ,f_{n}\right)\in C} 。

C {\displaystyle C} からの幾つかの関数に局所的に合致する M {\displaystyle M} の各点での各関数は、やはりまた C {\displaystyle C} に属する。

関連項目

接ベクトル空間

層 (数学)

ベクトル場

微分形式

代数多様体

脚注[脚注の使い方]^ 参照：坪井俊・東京大学大学院数理科学研究科教授の資料
^ Sikorski 1967


Sikorski, R. (1967). “Abstract covariant derivative”. Colloquium Mathematicum 18: 251?272. doi:10.4064/cm-18-1-251-272. 

参考文献.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-100{font-size:100%}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}

松島与三『多様体入門』裳華房〈数学選書, 5〉、1965年。.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}ISBN 9784785313050。 


小笠英志『多様体とは何か』講談社〈ブルー・バックス〉、2021年。 　一般向け入門書。　専門書を読む前か読み始めの時に読むと良いレベル。もしくは、専門書を読まないが多様体とはどういうものか知りたい人向け


関沢正躬『微分幾何学入門』日本評論社、2003年。ISBN 4535783845。 


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Hempel, John (1976). 3-Manifolds. Princeton University Press. ISBN 0-8218-3695-1 

Hirsch, Morris (1997). 3Differential Topology. Springer Verlag. ISBN 0-387-90148-5  - The most complete account, with historical insights and excellent, but difficult, problems. The standard reference for those wishing to have a deep understanding of the subject.

Kirby, Robion C.; Siebenmann, Laurence C. (1977). Foundational Essays on Topological Manifolds. Smoothings, and Triangulations. Princeton University Press. ISBN 0-691-08190-5  - A detailed study of the category of topological manifolds.

Lee, John M. (2000). Introduction to Topological Manifolds. Springer-Verlag. ISBN 0-387-98759-2 

Lee, John M. (2002), Introduction to Smooth Manifolds, Springer, ISBN 978-0-387-95448-6 

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