论文标题
Browder的定理：从一维参数空间到一般参数空间
Browder's Theorem: from One-Dimensional Parameter Space to General Parameter Space
论文作者
论文摘要
A parametric version of Brouwer's Fixed Point Theorem, which is proven using the fixed-point index, states that for every continuous mapping $f : (X \times Y) \to Y$, where $X$ is nonempty, compact, and connected subset of a Hausdorff topological space and $Y$ is a nonempty, convex, and compact subset of a locally-convex topological vector space, the set of fixed points $ f $，由$ c_f定义：= \ {（x，y）\ in x \ times y \ colon f（x，y）= y \} $，具有一个连接的组件，其对第一个坐标的投影为$ x $。在本说明中，我们使用将其减少到$ x = [0,1] $的情况下为此结果提供了基本证明。
A parametric version of Brouwer's Fixed Point Theorem, which is proven using the fixed-point index, states that for every continuous mapping $f : (X \times Y) \to Y$, where $X$ is nonempty, compact, and connected subset of a Hausdorff topological space and $Y$ is a nonempty, convex, and compact subset of a locally-convex topological vector space, the set of fixed points of $f$, defined by $C_f := \{ (x,y) \in X \times Y \colon f(x,y)=y\}$, has a connected component whose projection onto the first coordinate is $X$. In this note we provide an elementary proof for this result, using its reduction to the case $X = [0,1]$.
