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Mar30-11, 10:18 PM
Sci Advisor
P: 906
Quote Quote by michonamona View Post
Thank you for your replies.

Would it be safe to make the following generalization?

topological space--->metric space---->euclidean space

This means that every euclidean space is a metric space and every metric space is a topological space. By transitivity, every euclidean space is a topological space.
yes. certain spatial properties of euclidean space are abstracted to get the notion of a topological space.

metric spaces are in-between the two, they are a special kind of topological space, but there are several possible metrics on a given set, including R^n. of these, only one is the standard euclidean metric on R^n: d(x,y) = √(<x - y,x - y>).