System of Coincidence Theorems in Product Topological Spaces and Applications(Ⅰ)
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摘要: 首先引入了无凸性结构的有限连续拓扑空间(简称FC-空间)新概念.其次在FC-空间内建立了一个新的连续选择定理.应用此定理,在很弱的假设下,对定义在非紧FC-空间的乘积空间上的两个集值映射簇证明了某些新的重合点定理.这些结果推广了最近文献中的许多已知结果.某些应用将在后继文章中给出.Abstract: A new notion of finite continuous topological space (in short,FC-space) without convexity structure was introduced.A new continuous selection theorem was established in FC-spaces.By applying the continuous selection theorem,some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions.These results generalize many known results in recent literature.Some applications will be given in a follow-up paper.
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