Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil
Abstract:
We prove that the existence of positively expansive measures for continuous maps on compact metric spaces implies the existence of e > 0 and a sequence of (m, e)-separated sets whose cardinalities go to infinite as m→∞. We then prove that maps exhibiting such a constant e and the positively expansive maps share some properties.