metrizable space 中文意思是什麼
metrizable space
解釋
可度量化空間- metrizable : 可度量化的
- 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 ...
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In other words, d. burke and r. engelking and d. lutzer proved that a regular space is metrizable space if and only if it has a - hereditarily closure - preserving base in 1975, and introduced weakly hereditarily closure - preserving families, which proved that a regular k - space has - weakly hereditarily x closure - preserving bases is metrizable space, too
Burke ， r engelking和d lutzer證明了正則空間是可度量化空間當且僅當它具有遺傳閉包保持基，並引入了弱遺傳閉包保持集族（ weaklyhereditarilyclosure - preservingfamilies ） ，同時證明了具有弱遺傳閉包保持基的正則的k空間是可度量化空間。 -
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。 -
Completely metrizable space
完全可度量化空間
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