Locales, sublocales I

Stone duality leads naturally to the idea of locale theory.  Quickly said, the idea is that, instead of reasoning with topological spaces, we reason with frames.  The two concepts are not completely interchangeable, but the O ⊣ pt adjunction shows that they are close.  My purpose today is to give an introduction to what the analogue of a topological subspace should be on the localic side.  Read the full post.