In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （...In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （X）, on complete metric spaces.展开更多
In this paper,we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract,and that it also admits the uniform compact approximation property.These can be regarded as extensio...In this paper,we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract,and that it also admits the uniform compact approximation property.These can be regarded as extensions of Lindenstrauss and Kalton's corresponding results.展开更多
Let X be a metric space, f∈ C0(X), and V X. The set-trajectory ( V, f( V),…,fn(V)) is investigated and some conditions for f to have periodic points with given periods are obtained.
Taking domains in the one hand and actions of a semigroup （automaton） on the other, as two crucial notions in mathematics as well as in computer science, we consider the notion of compact directed complete poset （a...Taking domains in the one hand and actions of a semigroup （automaton） on the other, as two crucial notions in mathematics as well as in computer science, we consider the notion of compact directed complete poset （acts）, and investigate the interesting notion of absolute retractness for such ordered structures. As monomorphisms and embeddings for domain acts are different notions, we study absolute retractness with respect to both the class of monomorphisms and that of embed- dings for compact directed complete poset （acts）. We characterize the absolutely retract compact dcpos as complete compact chains. Also, we give some examples of compact di- rected complete poset acts which are （g-）absolutely retract （with respect to embeddings） and show that completeness is not a sufficient condition for （g-）absolute retractness.展开更多
The space of continuous maps from a topological space X to a topological space Y is denoted by C（X,Y）with the compact-open topology.In this paper we prove that C（X,Y）is an absolute retract if X is a locally compac...The space of continuous maps from a topological space X to a topological space Y is denoted by C（X,Y）with the compact-open topology.In this paper we prove that C（X,Y）is an absolute retract if X is a locally compact separable metric space and Y a convex set in a Banach space.From the above fact we know that C（X,Y）is homomorphic to Hilbert space l<sub>2</sub> if X is a locally compact separable metric space and Y a separable Banach space;in particular,C（R<sup>n</sup>,R<sup>m</sup>） is homomorphic to Hilbert space l<sub>2</sub>.展开更多
Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generaliz...Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.展开更多
文摘In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （X）, on complete metric spaces.
基金Support by National Natural Science Foundation of China(Grant Nos.11731010,12071389)。
文摘In this paper,we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract,and that it also admits the uniform compact approximation property.These can be regarded as extensions of Lindenstrauss and Kalton's corresponding results.
基金the Special Foundation of National Prior Basic Researches of China ( Grant No. G1999075108).
文摘Let X be a metric space, f∈ C0(X), and V X. The set-trajectory ( V, f( V),…,fn(V)) is investigated and some conditions for f to have periodic points with given periods are obtained.
文摘Taking domains in the one hand and actions of a semigroup （automaton） on the other, as two crucial notions in mathematics as well as in computer science, we consider the notion of compact directed complete poset （acts）, and investigate the interesting notion of absolute retractness for such ordered structures. As monomorphisms and embeddings for domain acts are different notions, we study absolute retractness with respect to both the class of monomorphisms and that of embed- dings for compact directed complete poset （acts）. We characterize the absolutely retract compact dcpos as complete compact chains. Also, we give some examples of compact di- rected complete poset acts which are （g-）absolutely retract （with respect to embeddings） and show that completeness is not a sufficient condition for （g-）absolute retractness.
基金This research is supported by the Science Foundation of Shanxi Province's Scientific Committee
文摘The space of continuous maps from a topological space X to a topological space Y is denoted by C（X,Y）with the compact-open topology.In this paper we prove that C（X,Y）is an absolute retract if X is a locally compact separable metric space and Y a convex set in a Banach space.From the above fact we know that C（X,Y）is homomorphic to Hilbert space l<sub>2</sub> if X is a locally compact separable metric space and Y a separable Banach space;in particular,C（R<sup>n</sup>,R<sup>m</sup>） is homomorphic to Hilbert space l<sub>2</sub>.
文摘Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.
