Liu Chuan, Lin Shou
Let K be a class of spaces which are eigher a pseudo-open s-image of a metric space or a k-space having a compact-countable closed k-network.Let K' be a class of spaces which are either a Fréchet space with a point-countable k-network or a point -Gδk-space having a compact-countable k-network.In this paper,we obtain some sufficient and necessary conditions that the products of finitely or countably many spaces in the class K or K' are a k-space.The main results are that
Theorem A If X,Y∈K.Then X×Y is a k-space if and only if (X,Y) has the Tanaka's condition.
Theorem B The following are equivalent :
(a) BF(ω2) is false.
(b) For each X,Y∈K',X×Y is a k-space if and only if (X,Y) has the Tanaka's condition.