Definition
6
[2F6]Any set \(X\) can be endowed with many different topologies. Here are two simple examples:
When a set \(X\) is endowed with the discrete topology, then all sets are open, and therefore closed. Equivalently, the discrete topology is caracterized by: every singleton is an open set.
When a set \(X\) is endowed with the indiscrete topology, then the only open (and, closed) sets are \(X,\emptyset \).