Title Dynamically defined topological entropy of co-compact open covers Type Article Keywords co-compact open set, dynamically defined co-compact entropy, topological dynamical system, genetic space. Abstract In this paper, the concept of dynamically defined topological entropy of co-compact open sets for iteration of a continuous system on non-compact Hausdorff space is introduced. Dynamically defined topological entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required). This is achieved through the consideration of a topological dynamic system and co-compact covers of the space. An example in the genetic space is presented Researchers Adel Gorouhi (First researcher)Mohammad Ebrahimi (Second researcher)Uosef mohammadi (Third researcher)