metrizable space meaning in English
可度量化空间
Examples
- A mapping theorem on sn - metrizable spaces
可度量化空间的映射定理 - Completely metrizable space
完全可度量化空间 - 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证明了正则空间是可度量化空间当且仅当它具有遗传闭包保持基，并引入了弱遗传闭包保持集族( weaklyhereditarilyclosure - preservingfamilies ) ，同时证明了具有弱遗传闭包保持基的正则的k空间是可度量化空间。 - 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
在文献[ 4 ]中，夏省祥引进了弱开映射，并研究了它和1 -序列覆盖映射的关系。本文在第二节研究了弱开映射与序列商映射，几乎开映射的关系，证明了有限到一的弱开映射保持g -第一可数空间；弱开闭映射保持g -度量空间。第三节研究了文献[ 5 ]中的一个例子，证明了完备映射不保持g -第一可数空间， g -度量空间， sn -第一可数空间， sn -度量空间。 - In this paper , we give a new characterization of metrizable spaces in terms of g - functions to answer nagata ' s question and equivalent characterizations of - spaces , spaces with - cp cs - network in terms of g - functions . we give weak g - functions as the generalizations of g - functions and cwbc - map , and we characterize some metrizable spaces in terms of weak g - functions
本文利用g -函数给出了度量空间的一个新刻划，回答了nagata的问题，并利用g -函数给出了-空间、具有- cpcs -网的空间的等价刻划，我们还将g -函数与cwbc -映射统一推广为弱g -函数，并利用弱g -函数刻划了一些度量空间。