**Date/Time**

Date(s) – 01/03/2017*3:00 pm – 4:00 pm*

**Location**

VG02

**Categories**

### Topologies and their specialization pre-orders

#### Abstract

Each topology induces a unique pre-order relation on the set: point x is ‘less or equal’ to point y if and only if x is in the closure of y. This pre-order, called a specialization pre-order, is not very interesting in Kolmogorov spaces (separation axiom T1 or above), because in this case it is just the equality relation. This is why specialization pre-orders have mostly been considered in computer science, such as the domain theory.

However, pre-orders also play an important role in economics as preference relations and in cosmology as causality relation. In this talk, we shall consider several properties of pre-orders and their corresponding topological properties, such as compactness, connectedness, countability, Baire category theorem and some others.