一维连通流形的分类（Ⅱ）

The Classification of 1-dimensional Connected Manifolds (Ⅱ)

连通的一维流形在同胚的意义之下恰可分成７类，它们分别以下列７个空间作为代表：１）紧致区间［０，１］；２）半实轴［０，∞）；３）实数轴Ｒ；４）单位圆周Ｓ１；５）超穷长半直线［０，ω１）；６）单向超穷长直线（－∞，ω１）；７）（双向）超穷长直线（－ω１，ω）．

In the sense of homeomorplnsm. all connected 1-dimensional manifolds can be divided into exact 7 classes. The following 7 spaces are representatives of them: 1)the compact interval I= [0, 1]:2) the real semi-axis[0. ∞):3) the real number ac R:4)the unit circle S1:5) the transfinitely long half straight line [0. ω1): 6) the unilaterally transfinitely long straight line (- ∞, ω1):7) the transfinitely long straight line(- ω1,ω1).