Tukey Order - Introduction

If $P$ and $Q$ are partially ordered sets, define Tukey order relation as follows: $P$ Tukey-dominates $Q$ if there is a map from $P$ to $Q$ that maps cofinal sets to cofinal sets. Suppose $X$ is a topological space, $M$ is a separable metric space and $K(Y)$ denotes collection of all compact subsets of $Y$. In this talk we will consider the case when $P=K(M)$ and $Q=K(X)$, both with inclusion relation, and will survey some basic results.