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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 $F_K(X,x_0)=[K,k_0; X,x_0]$.

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    Most likely, the set of relative homotopy classes of pointed maps. – 2017-01-09

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