关于一些弱于仿紧性质在连续闭映射下的逆象(Ⅰ)

In this paper, we study with uniform results the preimage of which the properties will preserve the same property under the continuous closed mapping whicd possess certain quite weak condition, for σ-metacompctness, θ-refinability, weakly θ-refinability, paralindel?fness, metalindelofness,δθ-refinability, weakly δθ-refinability, mesocompactness and sequentially mesocompactness, and so on. A necessary and sufficient condition about preimage problem, with uniform results, has been given in this paper; and therefore the results in D.K.Burke′s survey paper [4] have been strengthened in ihis paper.     

关于可数紧拓扑空间的基数

对于紧空间的势.优美的 cēch-pospi(?)il-Arhangelskii 定理指出:任何第一可数,紧T_2空间必是可数的或是有势2(?).本文讨论可数紧空间的势,所涉及到的概念及符号参见Kunen[2],Engnlking[1],凡提及的空间均要求 T_2分离性;全部结论不需要连续统假设 CH.     

关于一些弱于仿紧性质在连续闭映射下的逆象(1)

§0 引言 在如何减弱性质(P)使“性质(P) 列紧→紧”的研究中,许多数学家如G。Aguaro,J.M.Worrell,和H.H.Wicke等人一再减弱了性质(P)的条件,从而先后引入了一些弱于仿紧的空间性质。由[2],[5]等文,这些空间性质有如下蕴含关系: 仿紧→紧式仿紧[6]→CS式仿紧[6]→亚紧→θ加细[1]→弱θ加细[2]