Quick question. The metric does not metrize right? Specifically because it fails the triangle inequality.
P.S. Sorry about putting this in the wrong forum, the question arose in a topology setting but I can see how its more of an analysis question.
Extended real number line - Wikipedia, the free encyclopedia
But the sentence before can be interesting too. However, homeomorphisms represent a rude language to me So I'll leave it to you to understand that !There is no metric which is an extension of the ordinary metric on R.