Abstract
It is no secret to the observer that the new open sets play a role in general topology. and they represent research topic for many topologists in different parts of the world. In fact, there is an important topics in general topology and real analysis that deals with continuity of maps and their different forms by relying on new open set. In this work, we presented and studied a new class of continuous maps called T-continuous by using the concepts of T-open sets and T-closed sets, where important and basic properties of T-continuous map and its relationship with other maps were verified.
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