Topology

I am interested in topological spaces (in contrast to metric spaces) because they can capture multiple notions of "closeness".

The most basic object is a set. To make things concrete, let's consider the set of eviction complaints filed by landlords in Connecticut between February 2022 and October 2022. How's that for a concrete example?

Given this set, we can define a topology, \(\mathcal{T}\), which is a set whose elements consists of eviction complaints. That is, each element of the topology is a subset of the orginal set: \(A \in \mathcal{T}, A \subset X\). A topology must also include arbitrary unions of elements of the topology (referred to as open sets) and must include finite intersections of elements as well.