Abstract：A special topological space,namely the HF-space,was introduced in this paper,based on structuring HF-topology.It pointed out and demonstrated the identity of open set and closed set,and the relevance of HF-space and the minimum non-empty open set as well.Moreover,starting from the concept of the minimum non-empty open set,it also proved a series of significant theory,such as the necessity of the regularity of HF-space,normal space and locally connected space within HF-space;the unity of discrete space and T4-space;the trinity of Lindeloff space,A2-space and separable space;the trinity of Tychonoff space,Hausdorff space and T1-space.Perfect results among T1-space T2-space T3-space T3.5-space and T4-space within HF-space were derived in the end.
2012, Vol. 36 
