If X is a metric space, what is the simplest sufficient condition for d(x,y)<∞, ∀ x, y ∈ X?
But even with the standard metric, there is no Real M with d(x,y)<M for all x,y in ##\mathbb R^n ##Edit: Just choose the pair M,0 ( or generalized to n dimensions) for d(x,y).Sure. I was thinking about including infinite points and a non standard metric you mentioned.
What is the "standard" metric in Projective space? Is it the quotient metric?EDIT: Do we even know if the projective space is metrizable?That's why I said projective space. Can we keep the metric via the transition from circle to line, sphere to plane?
This is the standard case, don't know if there are many others "non-trivially" different: https://en.wikipedia.org/wiki/Non-Hausdorff_manifold#Line_with_two_origins :When it comes to topology I need to see. If possible step by step. Those people are notoriously counterintuitive.