Difference between revisions of "Homeomorphism"

Revision as of 17:59, 12 February 2015 (view source) Alec (Talk | contribs) ← Older edit		Revision as of 18:09, 12 February 2015 (view source) Alec (Talk | contribs) m Newer edit →
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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}}

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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

$$f:(X,\mathcal{J})\rightarrow(Y,\mathcal{K})$$ where:

1. $$f$$ is bijective
2. $$f$$ is continuous
3. $$f^{-1}$$ is continuous