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Two Notes on Topological Groups
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作者 ZHANG Ke-xiu LIU Xin TANG Zhong-bao 《Chinese Quarterly Journal of Mathematics》 2016年第1期82-86,共5页
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
关键词 topological group first-countable paratopological group locally feebly compact METRIZABLE
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About Compact and Sequentially Compact Coincide in Topological Groups with the Axiom (A_1) 被引量:1
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作者 Lina 《Northeastern Mathematical Journal》 CSCD 2004年第3期271-274,共4页
This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolp... This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolpgical group with the axiom (A1). 展开更多
关键词 topological space topological group COMPACT sequential compactness
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THE MAXIMUM OF THE γ-MAX-SUBADDITIVE FUNCTIONALS ON A CLASS OF TOPOLOGICAL GROUPS
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作者 定光桂 《Acta Mathematica Scientia》 SCIE CSCD 1998年第3期310-314,共5页
It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0... It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0, or 'lower semi-continuous' in some neighborhood V(x0) U0 and X is of second category; then p(x) can attain its supremum in U0. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if U0 is 'pseudo-bounded' set in X. 展开更多
关键词 γ-max-subadditive functional Binary fissionable topological group Pseudo bounded set.
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ALMOST PERIODICITY AND EQUICONTINUITY OF THE TOPOLOGICAL TRANSFORMATION GROUP 被引量:1
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作者 Li Zhicong Li Juntao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第4期467-472,共6页
In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf... In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous. 展开更多
关键词 uniform space topological transformation group EQUICONTINUITY almost periodicity compactly almost periodicity.
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The Non-countable Summation Type Hahn-Schur Theorems
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作者 LUETong-fu HUJian-hua CHOMin-hyung 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第2期137-140,共4页
The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In... The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true. 展开更多
关键词 rton-countable set SUMMATION Abelian topological group Hahn-Schur theorem
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Transversality on locally pseudocompact groups
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作者 Fucai LIN Zhongbao TANG 《Frontiers of Mathematics in China》 SCIE CSCD 2021年第3期771-782,共12页
Two non-discrete Hausdorff group topologiesτandδon a group G are called transversal if the least upper boundτ⋁δofτandδis the discrete topology.In this paper,we discuss the existence of transversal group topologi... Two non-discrete Hausdorff group topologiesτandδon a group G are called transversal if the least upper boundτ⋁δofτandδis the discrete topology.In this paper,we discuss the existence of transversal group topologies on locally pseudocompact,locally precompact,or locally compact groups.We prove that each locally pseudocompact,connected topological group satisfies central subgroup paradigm,which gives an affirmative answer to a problem posed by Dikranjan,Tkachenko,and Yaschenko[Topology Appl.,2006,153:3338–3354].For a compact normal subgroup K of a locally compact totally disconnected group G,if G admits a transversal group topology,then G/K admits a transversal group topology,which gives a partial answer again to a problem posed by Dikranjan,Tkachenko,and Yaschenko in 2006.Moreover,we characterize some classes of locally compact groups that admit transversal group topologies. 展开更多
关键词 Transversal group topology locally pseudocompact group locally compact group locally precompact connected space central topological group
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A Unified Convergence Theorem 被引量:2
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作者 JunDeWU JianWenLUO ShiJieLU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第2期315-322,共8页
We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent t... We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent to the Antosik-Mikusinski theorems. 展开更多
关键词 abelian topological group infinite matrix antosik-mikusinski theorems uniform convergence principles
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