POINTWISE PERIODIC SELF-MAPS OF SUBSPACES OF 2-DIMENSIONAL MANIFOLDS  

作　　者：麦结华 

机构地区：[1]Department of Mathematics, Guangxi University

出　　处：《Science China Mathematics》1990年第2期145-155,共11页中国科学：数学（英文版）

摘　　要：Let M be a 2-dimensional closed manifold, orientable or non-orientable. The construction of every compact locally connected subspace X of M without cut-points is analyzed. It is proved that every orientation-preserving (or reversing, or relatively preserving) point-wise periodic continuous self-map of X can be extended to a periodic self-homeomorphism of M (or of a 2-dimensional compact submanifold of M). In addition, every orientation-preserving (or reversing, or relatively preserving) pointwise periodic continuous self-map f of any path-connected subspace of M is proved to be a periodic self-homeomorphism, the number of the shorter-periodic points of f is shown to be finite, and generalization of Weaver’s conclusion is given.Let M be a 2-dimensional closed manifold, orientable or non-orientable. The construction of every compact locally connected subspace X of M without cut-points is analyzed. It is proved that every orientation-preserving (or reversing, or relatively preserving) point-wise periodic continuous self-map of X can be extended to a periodic self-homeomorphism of M (or of a 2-dimensional compact submanifold of M). In addition, every orientation-preserving (or reversing, or relatively preserving) pointwise periodic continuous self-map f of any path-connected subspace of M is proved to be a periodic self-homeomorphism, the number of the shorter-periodic points of f is shown to be finite, and generalization of Weaver's conclusion is given.

关 键 词：POINTWISE PERIODIC self-map pseudo-open disc left (right) side of a directed arc orientation-preserving (reversing) map lift of a homeomorphism. 

分 类 号：N[自然科学总论]