C–CONNECTED TOPOLOGICAL SPACES

In this work, we define a new notion of connectness which we name it C–connectedness. A triple (A, B, f) of nonempty open subsets A and B of R by the usual topology and a continuous function f : X → R is called a C–separation for a topological space X, providing X = f −1 (A∪ B) and A∩ B = A∩ B = ∅. X is called C–connected whenever, there is no any C–separation for it. A subset Y ⊆ X is called C–connected whenever as a subspace of X is C–connected. The notion of F–connectedness for topological spaces is generalized and as a consequence, the intermediate value theorem is extended. Also, some classical results about connectedness are generaized.