What does this notation mean in the Category of Pointed Sets

Question

I am curious what does $[K,k_0; X,x_0]$ mean in the Category of Pointed Sets.

The context is from Switzer's Algebraic Topology book:

Given a fixed pointed space $(K,k_0)\in\mathscr{PT}$, we define a function $F_K:\mathscr{PT}\to\mathscr{PS}$ as follows: for each $(X,x_0)\in\mathscr{PT}$ we take $F_K(X,x_0)=[K,k_0; X,x_0]$.

Answer 1

I found it in the previous chapter: $[X,x_0; Y,y_0]$ are homotopy classes of basepoint-preserving functions, where homotopies are rel $x_0$.