The Reverse of the Intermediate Value Theorem in Some Topological Spaces - Oussama Kabbouch; Mustapha Najmeddine (International Journal of Mathematics and Mathematical Sciences)
Any continuous function with values in a Hausdorff topological space has a closed graph and satisfies the property of intermediate value. However, the reverse implications are false, in general. In this article, we treat additional conditions on the function, and its graph for the reverse to be true.