Product Methods And G -Connectedness

The generalized topology on the Cartesian product of sets can be defined by the generalized topology on the factors of the product. A G-method on a set can derive a generalized topology, which is called a G-generalized topology. On the one hand, we introduce the concept of product G-methods on sets which lead to a G-generalized topology on the Cartesian products that is different both from the Csaszar and the Eckhoff product of G-generalized topologies on the factors. On the other hand, we study the G-connectedness of the Cartesian products and prove that a G-connectedness determined by an almost pointwise method is countably multiplicative. The countably multiplicative property of sequentially connected spaces is extended.