This note is devoted to study the preservation of connectedness under the basic operators in generalized topological spaces.
Some characterizations of generalized connectedness are given. As an application, we generalize some results in topological
We study the relationship between the product and other basic operations (namely σ, π, α and β) of generalized topologies. Also we discuss the connectedness, generalized connectedness and compactness of products of generalized
topologies. It is proved that the connectedness and compactness are preserved under the product of generalized topologies,
which shows that the definition of product of generalized topologies is quite reasonable.