I am working on some metric stuff for my intro real class. I'm having
a little trouble thinking about it. I have an interval on the real
line, say (a, b) I am to consider it as a metric space with the usual
distance in R.
My question is what the metric space consists of. Is the space the
interval and the metric happens to be the way distance is measured
there? Or does the metric define the space? Something like a set of
distances rather than set of points?
I'm just not sure.
