H-空间的覆盖性质及其应用
Covering Properties of H Spaces and Applications
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摘要: 我们得到了H-空间闭(开)覆盖性质的几个定理,改进和推广了Sperner.Klee,Alexandroff-Pasynkoff,Berge,Ghouila-Houri,Danzer-Grunbaum-Klee,Ky Fan,Shih-Tan,Horvath和Lassonde等人的相应结果.作为应用,我们对l.c.-空间内的下半连续集值映象证明了一个几乎不动点定理并且推广吉洪诺夫不动点定理到l.c.-空间.这些定理改进了Ky Fan和Horvath的相应结果.Abstract: Several theorems on closed(resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.
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Key words:
- covering property /
- H-space /
- H-convex /
- H-convex hull
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