Entropy of continuous maps on quasi-metric spaces

The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are associated to a given quasi-metric space are introduced and the entropy of a map of a given quasi-metric space and the maps of its associated metric spaces are compared. It is shown that the entropy of a map when symmetric properties is included is grater or equal to the entropy in the case that the symmetric property of the space is not considered.