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continuous_function [2014/07/09 15:05] nikolaj |
continuous_function [2014/10/26 13:59] nikolaj |
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| | @#FFBB00: definiendum | @#FFBB00: $ f\in \mathrm{it} $ | | | @#FFBB00: definiendum | @#FFBB00: $ f\in \mathrm{it} $ | | ||
| | @#AAFFAA: inclusion | @#AAFFAA: $ f:X\to Y $ | | | @#AAFFAA: inclusion | @#AAFFAA: $ f:X\to Y $ | | ||
| - | | @#FFFDDD: for all | @#FFFDDD: $y\in \mathcal{T}_Y$ | | + | | @#FFFDDD: for all | @#FFFDDD: $V\in \mathcal{T}_Y$ | |
| - | | @#55EE55: postulate | @#55EE55: $ f^{-1}(y)\in\mathcal{T}_X $ | | + | | @#55EE55: postulate | @#55EE55: $ f^{-1}(V)\in\mathcal{T}_X $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Theorems === | === Theorems === | ||
| - | A function to $\mathbb R^n$ is continuous iff all its components are. | + | A function to $\mathbb R^n$ is continuous iff all its components are. |
| + | |||
| + | >clarify topologies here | ||
| ==== Parents ==== | ==== Parents ==== | ||
| === Context === | === Context === | ||
| - | [[Topological space]], [[Inverse function]] | + | [[Topological space]] |
| - | === Refinement of === | + | === Requirements === |
| + | [[Inverse function]] | ||
| + | === Subset of === | ||
| [[Function]] | [[Function]] | ||
