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homeomorphism [2014/10/29 11:21] nikolaj |
homeomorphism [2014/10/29 21:13] (current) 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 | | ||
- | | @#55EE55: postulate | @#55EE55: $f,f^{-1}$ ... bijections, continuous | | + | | @#AAFFAA: inclusion | @#AAFFAA: $f$ ... bijection, continuous | |
+ | | @#55EE55: postulate | @#55EE55: $f^{-1}$ ... continuous | | ||
==== Discussion ==== | ==== Discussion ==== | ||
+ | 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]] | ||
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[[Topological space]] | [[Topological space]] | ||
=== Subset of === | === Subset of === | ||
- | [[Continuous function]], [[Bijective function]] | + | [[Bijective function]], [[Continuous function]] |