Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, October 27, 2014 - 12:00 to 12:45

Location:

Gilk 115

Abstract:

Given a finite set of n elements, how many possible topologies can be put on this set? While the number of finite topologies has been calculated for values up to n=18, there is no known formula (explicit or recursive) the number of topologies on a set of n elements in terms of n. In this talk we will look at the connection of this problem with open combinatorial problems in graph theory and order theory. We will also discuss a foundational theorem in this area which relates the number of total topologies on a finite set with the number of topologies satisfying the T_0 separation axiom. We will conclude with a discussion of various bounds, asymptotes, and partial results.