关于具有σ几乎局部有限基的拓扑空间

In 1983, ML Ito and K.Tamano introduced the notion of almost locally finiteness and investigated some properties of the class of spaces with a σ almost locally finite base. In this paper, some more results about such spaces are given . The main results are as follows:( 1 ) The image of a space with a σ -almost locally finite base under the finite to one closed map has a σ-almost locally finite base;( 2 ) The locally finite sum theorem holds for such spaces;( 3 ) A space X has a σ almost locally finite base if and only if X is a paracompact σ space and every closed subset of X has an almost locally finite open neighborhood base; (4)The monotonically normal space with an M-structure has a a σalmost localiy finite base.     

Stone-ech紧化的正则Wallman性质

J.van Mill曾证明了定理:多重点的集合仍为强N_1紧的强N_1紧空间的任意紧化都是正则Wallman的;特别地强N_1紧空间的Stone-Cech紧化是正则Wallman的.本文证明了可以用局部有限的强N_1紧开集族覆盖的正规空间的Stone-Cech紧化是正则Wallman的.从而就Stone-Cech紧化的情况改进了van Mill的结果.     

Stone-ech紧化的正则Wallman性质

J.van Mill曾证明了定理:多重点的集合仍为强N_1紧的强N_1紧空间的任意紧化都是正则Wallman的;特别地强N_1紧空间的Stone-Cech紧化是正则Wallman的.本文证明了可以用局部有限的强N_1紧开集族覆盖的正规空间的Stone-Cech紧化是正则Wallman的.从而就Stone-Cech紧化的情况改进了van Mill的结果.