On a property specific to the tent map

Let a set {X_λ; λ ∈ Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace X_λ to define a map g_Xλ : X_λ → 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 X_λ, λ ∈ Λ, we can find an initial point x₀ ∈ ω₀ such that {Mathematical expression}. The conditions are successfully applied to a closed cover of a weak self-similar set.