摘要
§1. Introduction If we denote by o （X） the number of all open subsets in X, I. Juhasz raised a famous question in[1] whether o （X）ω= o GX) for every infinite strongly Hausdorff space. In the same paper, he alsoproved that it is true for T3hereditarily paracompact spaces or topological groups. In [2], VanDouwen and Zhou Hao-Xuan showed it is true for perfectly normal spaces and suggested thequestion of whether it holds for any hereditarily normal space X. On the other hand, we know from[4] that paracompactness can be characterized by collectionwise normality （CWN） θ-refinability
1. Introduction If we denote by o （X） the number of all open subsets in X, I. Juhasz raised a famous question in[1] whether o （X）ω= o GX) for every infinite strongly Hausdorff space. In the same paper, he alsoproved that it is true for T3hereditarily paracompact spaces or topological groups. In [2], VanDouwen and Zhou Hao-Xuan showed it is true for perfectly normal spaces and suggested thequestion of whether it holds for any hereditarily normal space X. On the other hand, we know from[4] that paracompactness can be characterized by collectionwise normality （CWN） θ-refinability
