Local expansions on graphs and order of a point (Q1819775)

A continuous function f from a metric space (X,\(\rho)\) to a metric space (Y,d) is said to be a local expansion provided, for each point \(x\in X\), there is a neighborhood U of x and a positive number M such that, for all pairs y,z\(\in U\), d(f(y),f(z))\(\geq M\cdot \rho (y,z)\). The paper considers expansive maps on linear graphs and derives relationships between the cyclic order, the tree order, and the order of a point x and its image f(x). Generally, the cyclic order is not decreased and, for open expansive maps, the three orders are preserved.