It's hard to think of a non-trivial example of trivial quasiorder. Define by . It's trivially trivial, but what you gonna do?Originally Posted by nweissma
A neighborhood of a point x is any open set containing x. I've never heard of a specialization quasiorder.
There are valid topologies where a singleton is an open set. One example is the discrete topology where every set is an open set. It's a theorem that a topology satisfies the separation axiom iff every set containing a single point is closed.