On the Extensions of Continuous Functions from Dense Subspaces
R. Blefko, S. Mrowka · Proceedings of the American Mathematical Society · 1966
Recently Taimanov and McDowell have been concerned with the question: when can a continuous function from a space A to a compact space F be extended to a space aX in which X is dense?An important result, e.g., obtained by Taimanov is the following Theorem.Let X be dense in the Pi-space aX.Then in order that a continuous function f from X into a compact space Y have a continuous extension f*: aX-> Y it is necessary and sufficient that for each two disjoint closed sets Pi and F2, /-1[P] awd/-1[p2] have disjoint closures in