Having never read Munkres (completely), I got lost about half way through what you are writing but here's how I would look at it.
Generally speaking, the boundary of an n dimensional set has dimension n-1. That is the surface of a three dimensional object is two dimensional and the boundary of a two dimensional object is one dimensional (a curve). The boundary of a curve consists of its two endpoints: and points have dimension 0. The boundary of a finite set of points is the empty set: the dimension of the empty set is defined to be -1 in order to continue that pattern.