Metric spaces

• How to Prove Inequalities for Infima and Suprema
  The title does not specify an inequality, so this article proves a standard one: the difference of two infima is bounded by the supremum of the pointwise difference.
• Is Every Singleton Set Open? (No, Here's When It Is)
  Singleton sets are not open in general. In ℝ, {0} is closed but not open. A singleton {x} is open exactly when x is an isolated point, as in discrete spaces.
• Why Is Every Singleton Set Open in a Finite Metric Space?
  Proof that {x} is open in any finite metric space, using the minimum distance to the other points, and why this makes every subset open (the discrete topology).