EDB — 0MX

Exercises

1. [0MX]We generalize the definition of metric space assuming that \(d:X→[0,∞]\) (the other axioms are the same). Show that the relation \(x∼ y\) defined by

   \[ x∼ y\iff d(x,y){\lt}∞ \]

   is an equivalence relation, and that equivalence classes are open, and therefore are disconnected from each other.

   Solution 1

   [0MY]↺↻