... 同伦的等价 equivalence of homotopy 同伦定理 homotopy theorem 同伦关系 relation of homotopy ...
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本文利用连续同伦方法讨论非线性映射在有界区域内零点的存在性和零点数目，以及推广若干经典定理。
With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.
其次，为使此定理的应用变得直接简便，我们还给出了关于拓扑空间（组）之间同伦等价的几个命题。
Secondly, in order to favor utilizing this theorem, several propositions are given on the homotopy equivalence between two topological space sets.
其次给出一个不用约当曲线定理而仅用同伦曲线概念的更为简洁的证法。
Next, we give a briefer proof that USES the concept of homotopy of curves, In this course of the proof, we don't use the theorem of Jordan curves.
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