论文标题
可亲且几乎和ami可亲的固定组。 Brouwer固定点定理的扩展
Amiable and Almost Amiable Fixed Sets. Extension of the Brouwer Fixed Point Theorem
论文作者
论文摘要
本文以CW的描述性接近形式（闭合 - 限制弱）空间作为可亲的固定子集的来源以及描述性近端连续图（DPC）地图的几乎可亲的固定子集引入了形状边界区域。 DPC地图是V.A.在1950年代初期引入的Efremovič-Smirnov近端连续（PC）地图的扩展。 Efremovič和Yu。 M. Smirnov。可亲的固定集和其自由Abelian组表示的Betti数字是DPC相对于集合边界区域的描述得出的。几乎和固定的固定集来自DPC，通过放松匹配的描述要求，以实现集合的描述性接近度。这种宽松的固定组的轻松形式适用于固定集的紧密度大致而不是精确的应用。以宽带的方式给出了许多可亲固定组的例子。这项工作的双重产品是Jordan曲线定理和固定细胞复合物定理的变体，该定理是Brouwer固定点定理的扩展。
This paper introduces shape boundary regions in descriptive proximity forms of CW (Closure-finite Weak) spaces as a source of amiable fixed subsets as well as almost amiable fixed subsets of descriptive proximally continuous (dpc) maps. A dpc map is an extension of an Efremovič-Smirnov proximally continuous (pc) map introduced during the early-1950s by V.A. Efremovič and Yu. M. Smirnov. Amiable fixed sets and the Betti numbers of their free Abelian group representations are derived from dpc's relative to the description of the boundary region of the sets. Almost amiable fixed sets are derived from dpc's by relaxing the matching description requirement for the descriptive closeness of the sets. This relaxed form of amiable fixed sets works well for applications in which closeness of fixed sets is approximate rather than exact. A number of examples of amiable fixed sets are given in terms of wide ribbons. A bi-product of this work is a variation of the Jordan Curve Theorem and a Fixed Cell Complex Theorem, which is an extension of the Brouwer Fixed Point Theorem.
