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homeomorphism [2014/10/29 21:12] nikolaj |
homeomorphism [2014/10/29 21:13] nikolaj |
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| | @#55CCEE: context | @#55CCEE: $\langle X,\mathcal{T}_X\rangle, \langle Y,\mathcal{T}_Y\rangle$ ... topological spaces | | | @#55CCEE: context | @#55CCEE: $\langle X,\mathcal{T}_X\rangle, \langle Y,\mathcal{T}_Y\rangle$ ... topological spaces | | ||
| | @#FFBB00: definiendum | @#FFBB00: $f\in$ it | | | @#FFBB00: definiendum | @#FFBB00: $f\in$ it | | ||
| - | | @#AAFFAA: inclusion | @#AAFFAA: $f$ ... invertible, continuous | | + | | @#AAFFAA: inclusion | @#AAFFAA: $f$ ... bijection, continuous | |
| | @#55EE55: postulate | @#55EE55: $f^{-1}$ ... continuous | | | @#55EE55: postulate | @#55EE55: $f^{-1}$ ... continuous | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | Homeomorphisms are continuous bijections. | + | A homeomorphism is a bijection which is continuous in both directions. |
| === Reference === | === Reference === | ||
| Wikipedia: [[https://en.wikipedia.org/wiki/Homeomorphism|Homeomorphism]] | Wikipedia: [[https://en.wikipedia.org/wiki/Homeomorphism|Homeomorphism]] | ||
| Line 14: | Line 15: | ||
| [[Topological space]] | [[Topological space]] | ||
| === Subset of === | === Subset of === | ||
| - | [[Continuous function]], [[Bijective function]] | + | [[Bijective function]], [[Continuous function]] |
