general topological space 中文意思是什麼

general topological space 解釋
一般拓撲空間
  • general : adj （opp special）1 一般的，綜合的，通用的。2 普通的，廣泛的，通常的。3 全體的，總的；全面的，普...
  • topological : 拓撲的
  • space : n 1 空間；太空。2 空隙，空地；場地；（火車輪船飛機中的）座位；餘地；篇幅。3 空白；間隔；距離。4 ...
  1. It is a main task of general topology to compare different spaces. mappings which connect different spaces are important tools to complete it. which mapping preserves some special generalized metric space is a basic probleme in investigating generalized metric spaces by mappings. g - first countable spaces and g - metri / able spaces have many important topological properities so to investigate which mapping preserves them is very necessary. in [ 7 ], clnian liu and mu - ming dai prove that open - closed mappings preserve g - metri / able spaces ; whether open mappings preserve g - first countable spaces is an open probleme asked by tanaka in [ 6 ]. in [ 4 ], sheng - xiang xia introduces weak opewn mappings and investigates the relations between them and 1 - sequence - covering mappings. in the second section of this article, we investigate weak open mappings have the relations with other mappings and prove that the finite - to - one weak open mappings preserve g - first countable, spaces and weak open closed mapping preserve g - metrizable spaces. in the third section, we investigate an example to show that perfect mappings do not preserve g - first countable spaces, g - metrizable spaces, sn - first countable spaces and sn - metrizable spaces

    在文獻[ 4 ]中，夏省祥引進了弱開映射，並研究了它和1 -序列覆蓋映射的關系。本文在第二節研究了弱開映射與序列商映射，幾乎開映射的關系，證明了有限到一的弱開映射保持g -第一可數空間；弱開閉映射保持g -度量空間。第三節研究了文獻[ 5 ]中的一個例子，證明了完備映射不保持g -第一可數空間， g -度量空間， sn -第一可數空間， sn -度量空間。
  2. Further, general procedure of this method is summarized. finally, the connection between topological transformation reasoning function and uniform space is studied. in addition, the group in uniform space is created

    最後，討論了拓撲變換推理函數關系與一致空間的聯系，構造出一致空間的群結構，這為構造推理函數提供了一定的理論基礎與方法。
  3. According to the dirac constrain theory and the extended condition, we deduce the gauge generators, show the brst transformation of ( 1 + 1 ) dimension o ( 3 ) non - linear model under the new general condition. we first gain the new general commutation relations of ghost field, deduce the brst charge from gauge generator, complete the general brst quantization of the model, get green function, connecting green function and generating functional, gain three kinds of ward identities. at last, we complete the brst quantization of o ( 3 ) non - linear model with topological term in ( 1 + 1 ) dimensions space - time

    最後依據dirac約束規范理論和推廣的條件，導出了規范生成元，推導出了1 + 1維o （ 3 ）非線性模型的新的一般條件下的brst變換，給出了其brst變換與dirac規范變換的等價性，首次得到了鬼場的一般對易關系，且其一般參數為零時就回到通常的鬼場的對易關系，第一次由規范生成元導出了brst荷，進而完成了此模型的一般的brst量子化，並在此基礎上進一步導出了此系統的green函數、連通green函數生成泛函和正規頂角生成泛函，獲得了三種不同的ward恆等式。
  4. Reich [ 2 ] proved the ergodic theorems to nonexpansive semigroups in hilbert spaces. takahashi and zhang [ 3 ], tan and xu [ 4 ] extended baillon ' s theorem to asymptotically nonexpansive and asymptotically nonexpansive type semigroups in hilbert spaces. recently, reich [ 6 ], bruck [ 5 ], oka [ 7 ] gave the ergodic convergence theorems for nonexpansive, asymptotically nonexpansive mappings and semigroups in uniformly convex banach spaces with frechet differentiable norm. li and ma [ 13 ] obtained the ergodic convergence theorems for general commutative asymptotically nonexpansive type topological semigroups in reflexive banach space, which is a great breakthrough

    Baillon [ 1 ]首先在hilbert空間的非空凸閉子集上給出了非擴張映照的弱遍歷收斂定理。 baillon的定理引起了很多數學家的興趣， reich [ 2 ]在hilbert空間中證明了非擴張半群的遍歷收斂定理。 takahashi和zhang [ 3 ] ， tan和xu [ 4 ]分別將baillon的定理推廣到漸近非擴張半群及漸近非擴張型半群。
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