New types of chaotic maps on topological spaces

In this paper, we will define a new class of chaotic maps on locally compact Hausdorff spaces called λ-type chaotic maps defined by λ-type transitive maps. This new definition implies John Tylar definition which coincides with Devanney’s definition for chaos when the topological space happens to be a metric space. Relationships with some other type of chaotic maps are given. Further, we have proved that topological λ-type transitivity implies λ-dense orbits in a space X where X is a non-empty locally λ-compact Hausdorff topological space.