In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.
In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a ...In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.展开更多
We show that the completion of a partial metric space can fail be unique,which answers a question on completions of partial metric spaces.In addition,to this paper discusses metrizability around partial metric spaces.
This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces.In this paper,the uniformity and properties far generalized H-space are consi...This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces.In this paper,the uniformity and properties far generalized H-space are considered.The conditions of metrization and the form of metric functions for generalized H-spaces,H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented.The results of this paper generalize and unify some recent results of[1-2,8,10].展开更多
The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the ...The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.展开更多
SINCE Michael (1952) published the first book about topological algebras, it has become abranch of functional analysis. Applications of topological algebras have been found in complexanalysis of several variables, dif...SINCE Michael (1952) published the first book about topological algebras, it has become abranch of functional analysis. Applications of topological algebras have been found in complexanalysis of several variables, differential geometry, unbounded operator and others, and alge-braic topology, k-theory and others have been applied to topological algebras (see, for exam-ple, ref.[2]). It is well known that the set of all continuous linear operators on Banach spaceconstitutes a Banach algebra, so it is obviously meaningful to study the topological algebra con-stituted by the set of all continuous linear operators on concrete topological vector space. It展开更多
Based on the modern development of Metrization theorem for context,the main results obtained in recent ten years on point-discrete families are summarized.This paper mainly introduces the theory of the spaces with opo...Based on the modern development of Metrization theorem for context,the main results obtained in recent ten years on point-discrete families are summarized.This paper mainly introduces the theory of the spaces with opoint-discrete bases,the spaces with certain o-point-discrete networks,and the relationship between the above spaces and the spaces with certain o-compactfinite networks.展开更多
文摘In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.
基金Supported by the National Natural Science Foundation of China(11201414,11471153)
文摘In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.
基金This project is supported by the National Natural Science Foundation of China(11801254,61472469,11461005).
文摘We show that the completion of a partial metric space can fail be unique,which answers a question on completions of partial metric spaces.In addition,to this paper discusses metrizability around partial metric spaces.
文摘This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces.In this paper,the uniformity and properties far generalized H-space are considered.The conditions of metrization and the form of metric functions for generalized H-spaces,H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented.The results of this paper generalize and unify some recent results of[1-2,8,10].
文摘The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.
文摘SINCE Michael (1952) published the first book about topological algebras, it has become abranch of functional analysis. Applications of topological algebras have been found in complexanalysis of several variables, differential geometry, unbounded operator and others, and alge-braic topology, k-theory and others have been applied to topological algebras (see, for exam-ple, ref.[2]). It is well known that the set of all continuous linear operators on Banach spaceconstitutes a Banach algebra, so it is obviously meaningful to study the topological algebra con-stituted by the set of all continuous linear operators on concrete topological vector space. It
文摘Based on the modern development of Metrization theorem for context,the main results obtained in recent ten years on point-discrete families are summarized.This paper mainly introduces the theory of the spaces with opoint-discrete bases,the spaces with certain o-point-discrete networks,and the relationship between the above spaces and the spaces with certain o-compactfinite networks.
