Can say me why annulus and circle are not homeomorphic?

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SUMMARY

The annulus and the circle are not homeomorphic due to their differing topological properties. Specifically, removing two points from a circle results in two disconnected components, while removing any two points from an annulus maintains its connectedness. This fundamental difference in connectivity confirms that these two shapes cannot be transformed into one another through continuous deformation.

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Can say me why annulus and circle are not homeomorphic?
 
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Hi Seydunas, :smile:

The easiest way to see this is with so called "dispersion points". Removing two points from the circle gives you two connected components, thus it becomes disconnected. But from the annulus, you can remove any two points, and the result remains connected.

This means that the circle and the annulus are not homeomorphic.
 


Owwwww, yes, i have tried to remove only one point but this did not give me any solution. Thank you micromass.
 

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