Definition talk:Euclidean Space

It occurred to me that this page already exists, as a Proof (as opposed to a Definition).

If this page is just redirected to the Proof page, would that make the definition count wrong? Does it matter? --Matt Westwood 11:20, 11 January 2009 (UTC)
 * I'm going to reply on your talk page, since this article is already redirected. Zelmerszoetrop 13:06, 11 January 2009 (UTC)

I was hasty - I've un-redirected the original definition page. I'll leave this be for the moment and get on with all that tedious analysis stuff ... --Matt Westwood 14:25, 11 January 2009 (UTC)

Definition properties
At base, the definition that I have is that a "Euclidean space" is the metric space formed by the vector space $\R^n$ with the Euclidean metric on it. The other properties on top (addition, scalar multiplication, all that stuff) follow as properties of that structure. Therefore there is no need to state them as necessary properties of this object. If it is considered necessary to alert the user to all these properties immediately on hitting this page, then IMO they should be indicated in the "Also see" section.

Or am I wrong, and that it is necessary to define all these properties up front (i.e. they do not naturally follow from the properties of the vector space $\R^n$ and need to be stated separately) then I think I need to go back to school. --prime mover 02:15, 18 March 2012 (EDT)