%0 Journal Article
%T 拓扑学中的同伦与基本群<br>Homotopy and Fundamental Group in Topology
%A 杨秋花
%A 李进友
%J Pure Mathematics
%P 36-45
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.153074
%X 本文主要研究拓扑空间中同伦的相关性质&#65292;进而讨论道路的逆及乘法运算&#65292;由此得到基本群&#65292;通过证明知基本群为拓扑不变量&#65292;最后利用基本群证明二维球面<i>S</i><sup>2</sup>不同胚于环面<i>T</i><sup>2</sup>。<br>This article mainly studies the relevant properties of homotopy in topological spaces, and then discusses the inverse and multiplication operations of roads, thereby obtaining the fundamental group. By proving that the known fundamental group is a topological invariant, the fundamental group is finally used to prove that the two-dimensional sphere<i> S</i><sup>2</sup> is different from the torus<i> T</i><sup>2</sup>.
%K 拓扑空间&#65292
%K 同伦&#65292
%K 道路&#65292
%K 道路类&#65292
%K 基本群<br>Topological Space
%K Homotopy
%K Road
%K Road Class
%K Basic Group
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=109040