## cone metric space [closed]

my question is why it is named "cone" metric space .Is there any geometrical meaning for that ..one thing that cone is in three dimensional . but we can define cone metric space for any set with co-domain is real banach and cone in that.

whether cone in three dimensional is projected to two dimensional

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I'm afraid your question is not appropriate for this site, so I'm closing it. In mathematics, the word "cone" is not restricted to three dimensional objects. – S. Carnahan Jan 24 2011 at 14:43
Or, it sure doesn't look appropriate. You might have more success on Math Overflow if you took more trouble with formulating your question; the phrases "one thing that cone is in three dimensional" and "whether cone in three dimensional is projected to two dimensional" are ungrammatical, and seem close to gibberish. A quick answer to your first question is that it's a set with a distance function which is valued in a real Banach space E which is partially ordered with respect to a cone in E, or so I gather after a quick consultation with google. Seems pretty straightforward to me. – Todd Trimble Jan 24 2011 at 14:51