The construction of P-expansive maps of regular continua: A geometric approach

In this paper, we prove the following: Let G be a graph, f :G→G a continuous map and P a finite subset of G such that f(P)⊂P. Then there exist a regular continuum Z, a continuous map g :Z→Z and a semi-conjugacy π :G→Z such that is π(P)-expansive, and p,q∈P and Q is a subset of P with A∩Q≠∅ for any arc A in G between p and q, then A′∩π(Q)≠∅ for any arc A′ in Z between π(p) and π(q). ition, f is point-wise P-expansive if and only if π|P is one-to-one. s paper we are especially interested in the geometrical structure of Z. Actually we can see the complicated construction of Z.