第一可数空间的英文

first-countable space

• 第一:    first; primary; fo ...
• 可:    approve
• 数:    frequently; repeat ...
• 空间:    space; enclosure; ...

例句与用法

1. It is a main task of general topology to compare different spaces . mappings which connect different spaces are important tools to complete it . which mapping preserves some special generalized metric space is a basic probleme in investigating generalized metric spaces by mappings . g - first countable spaces and g - metri / able spaces have many important topological properities so to investigate which mapping preserves them is very necessary . in [ 7 ] , clnian liu and mu - ming dai prove that open - closed mappings preserve g - metri / able spaces ; whether open mappings preserve g - first countable spaces is an open probleme asked by tanaka in [ 6 ] . in [ 4 ] , sheng - xiang xia introduces weak opewn mappings and investigates the relations between them and 1 - sequence - covering mappings . in the second section of this article , we investigate weak open mappings have the relations with other mappings and prove that the finite - to - one weak open mappings preserve g - first countable , spaces and weak open closed mapping preserve g - metrizable spaces . in the third section , we investigate an example to show that perfect mappings do not preserve g - first countable spaces , g - metrizable spaces , sn - first countable spaces and sn - metrizable spaces
   在文献[ 4 ]中，夏省祥引进了弱开映射，并研究了它和1 -序列覆盖映射的关系。本文在第二节研究了弱开映射与序列商映射，几乎开映射的关系，证明了有限到一的弱开映射保持g -第一可数空间；弱开闭映射保持g -度量空间。第三节研究了文献[ 5 ]中的一个例子，证明了完备映射不保持g -第一可数空间， g -度量空间， sn -第一可数空间， sn -度量空间。

百科释义

在拓扑学上，第一可数空间（First-countable space）是指有可数的局部基的拓扑空间，即对于x in X，存在x的开邻域序列U_1,U_2,U_3,...，使得对于任意的邻域V，存在整数i使得U_i subseteq V。