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chart [2014/10/29 21:01] nikolaj |
chart [2014/11/08 16:35] nikolaj |
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| @#55CCEE: context | @#55CCEE: $n\in \mathbb N$ | | | @#55CCEE: context | @#55CCEE: $n\in \mathbb N$ | | ||
| @#BBDDEE: let | @#BBDDEE: $\langle \mathbb R^n,T_{\mathbb R^n}\rangle$ ... Euclidean topology | | | @#BBDDEE: let | @#BBDDEE: $\langle \mathbb R^n,T_{\mathbb R^n}\rangle$ ... Euclidean topology | | ||
- | | @#FFBB00: definiendum | @#FFBB00: $\phi\in$ it | | + | | @#FFBB00: definiendum | @#FFBB00: $\langle U,\phi\rangle\in$ it | |
- | | @#FFFDDD: exists | @#FFFDDD: $U_X\in T_M$ | | + | | @#AAFFAA: inclusion | @#AAFFAA: $U\in T_M$ | |
| @#FFFDDD: exists | @#FFFDDD: $U_{\mathbb R^n}\in T_{\mathbb R^n}$ | | | @#FFFDDD: exists | @#FFFDDD: $U_{\mathbb R^n}\in T_{\mathbb R^n}$ | | ||
- | | @#AAFFAA: inclusion | @#AAFFAA: $\phi:U_M\to U_{\mathbb R^n}$| | + | | @#AAFFAA: inclusion | @#AAFFAA: $\phi:U\to U_{\mathbb R^n}$| |
| @#AAFFAA: inclusion | @#AAFFAA: $\phi$ ... homeomorphism | | | @#AAFFAA: inclusion | @#AAFFAA: $\phi$ ... homeomorphism | | ||
==== Discussion ==== | ==== Discussion ==== | ||
- | The charts on $\langle M$ are the homeomorphism into $\mathbb R^n$. | + | The charts on $M$ are the homeomorphism into $\mathbb R^n$. |
==== Parents ==== | ==== Parents ==== |