The Reverse of the Intermediate Value Theorem in Some Topological Spaces

Oussama Kabbouch, Mustapha Najmeddine, Frédéric Mynard
2021 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.
doi:10.1155/2021/6320969 fatcat:loe4qpjrhjehhcydqatfsvmty4