I Homeomorphism onto a not open image in the target

cianfa72
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An example of homeomorphism onto the image that isn't open in the target
Can you provide an example of homeomorphism onto the image φ:U→φ(U) where the image φ(U)⊂M is not open in M w.r.t. its assigned topology ?

Thanks.
 
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cianfa72 said:
TL;DR Summary: An example of homeomorphism onto the image that isn't open in the target

Can you provide an example of homeomorphism onto the image φ:U→φ(U) where the image φ(U)⊂M is not open in M w.r.t. its assigned topology ?

Thanks.
Take a subset ##U\subset M##, which is not open and the identity map.
 
martinbn said:
Take a subset ##U\subset M##, which is not open and the identity map.
Ah ok, you mean a not open ##U \subset M## topologized with the subspace topology from ##M## taken as domain of the identity map ##I_d## (homeomorphism onto the image ##I_d(U)## w.r.t. the subspace topology from ##M##).
 
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