On a property specific to the tent map

Let a set {Xλ; λ Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace Xλ to define a map gXλ:Xλ→X which has the following property specific to the tent map known in the baker’s transformation. Namely, for any infinite sequence ω0, ω1, ω2, … of Xλ, λ Λ, we can find an initial point x0 ω0 such that gω0(x0) ω1,gω1(gω0(x0)) ω2,…. The conditions are successfully applied to a closed cover of a weak self-similar set.