چكيده فارسي :
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.
