Difference between revisions of "Homeomorphism"
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# <math>f</math> is [[Bijection|bijective]] | # <math>f</math> is [[Bijection|bijective]] | ||
| − | # <math>f</math> is [[Continuous|continuous]] | + | # <math>f</math> is [[Continuous map|continuous]] |
| − | # <math>f^{-1}</math> is [[Continuous|continuous]] | + | # <math>f^{-1}</math> is [[Continuous map|continuous]] |
{{Definition|Topology}} | {{Definition|Topology}} | ||
Revision as of 18:09, 12 February 2015
Not to be confused with "Homomorphism"
Topological Homeomorphism
A topological homeomorphism is bijective map between two topological spaces [math]f:(X,\mathcal{J})\rightarrow(Y,\mathcal{K})[/math] where:
- [math]f[/math] is bijective
- [math]f[/math] is continuous
- [math]f^{-1}[/math] is continuous
