metric topology 中文意思是什麼
metric topology
解釋
度量拓撲-
In the research and development of general topology the metriz - able problem of the topological spaces was a central task interminally, this is because that metric spaces have a lot of good proverties, and they have important application in the field of math
在一般拓撲學的研究和發展中，拓撲空間的可度量化問題始終是一個中心課題，這是因為度量空間具有許多良好的性質，在數學領域內有著重要的應用。 -
So far, mathematicians who study topology have obtained substantial achievements in important topological directions, such as generalized metric space, cardinal function, compactness, dimension theory, etc. but what is worth to paying attention to is that we often draw on one special type of topological space to think and solve problems, for example, the classical structures, sorgenfrey line k, michael line rq, niemytzki planetv, kxk, # q xp, etc. ; subtle and profound topological properties aredetailedly characterized by them
而值得注意的是，在一般拓撲學的研究歷史中，我們常常藉助一類特殊的空間來思考和解決問題，如我們熟悉的經典構造： sorgenfrey直線k 、 michael直線r _ q 、 niemytzki平面n 、 k k 、 r _ q p等等，漂亮地刻畫了細微而深奧的拓撲性質。 -
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。 -
The paper do n ' t attempt to definite new generalized metric space classes and new covers and mappings. this is because in the development of revent several decades in topology, the space classes were definited by all sorts of formal generalizations have reached a flooded extent, continual introduction of new spaces and over tiny division have made topology develop to an empty theorical margin
本文不試圖去定義新的廣義度量空間類以及新的覆蓋與映射，這是因為近幾十年拓撲學的發展，各種形式的「推廣」所定義的空間類已達到泛濫的程度，新空間的不斷引入，過細的劃分使得拓撲學似乎發展到了空洞的理論邊緣。
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