Let Γ be a compact d-set in Rn with 0 < d ≤n, which includes various kinds of fractals. The author shows that the Besov spaces Bspq(Γ) defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding Γ as a space of homogeneous type when 0 < s < 1, 1 < p <∞　 and 1≤q≤∞.