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## Main Question or Discussion Point

Hi all,

I need help with a paragraph of my book that I don't understand. It says: "the map sending all of ℝ^n into a single point of ℝ^m is an example showing that a continuous map need not send open sets into open sets".

My confusion arising because I can't figure out how this map can be continuous, since the definition is:

" a map is continuous if the inverse image of an open set of the range is an open set". In this case it seems that a single point of R^m isn't an open set, so how can we talk about continuity?

Thanks in advance.

Diego.

I need help with a paragraph of my book that I don't understand. It says: "the map sending all of ℝ^n into a single point of ℝ^m is an example showing that a continuous map need not send open sets into open sets".

My confusion arising because I can't figure out how this map can be continuous, since the definition is:

" a map is continuous if the inverse image of an open set of the range is an open set". In this case it seems that a single point of R^m isn't an open set, so how can we talk about continuity?

Thanks in advance.

Diego.