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An Elementary Overview of Mathematical Structures最新文献

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Topological structures, I 拓扑结构
An Elementary Overview of Mathematical Structures Pub Date : 2020-08-18 DOI: 10.1142/9789811220326_0004
H. Herrlich
{"title":"Topological structures, I","authors":"H. Herrlich","doi":"10.1142/9789811220326_0004","DOIUrl":"https://doi.org/10.1142/9789811220326_0004","url":null,"abstract":"The concept of a topological space has been a prime object of topological investigations. Unfortunately it suffers from certain deficiencies such as : (a) The category Top of topological spaces and continuous maps is not as well behaved as one would like it to be; e.g., Top is not cartesian closed, i.e., it is not possible to supply for any pair {X9 Y) of topological spaces the set X Y of all continuous maps from Y to X with a topology such that {X) is naturally isomorphic to X*. Also, in Top the product of quotient maps in general is no longer a quotient map. (b) Several important concepts of a topological nature—such as uniform convergence, uniform continuity, and completeness—cannot be expressed in the framework of the theory of topological spaces. There have been serious efforts by prominent mathematicians to remedy this situation. But none of the solutions offered is free from all the deficiencies mentioned above. The purpose of this note is to stimulate discussion on these matters among point set topologists.","PeriodicalId":427744,"journal":{"name":"An Elementary Overview of Mathematical Structures","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120830930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
Algebraic structures, II 代数结构，2
An Elementary Overview of Mathematical Structures Pub Date : 2020-08-18 DOI: 10.1142/9789811220326_0003
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引用次数: 0
Categorical limits and adjunctions 范畴限制和补语
An Elementary Overview of Mathematical Structures Pub Date : 2020-08-18 DOI: 10.1142/9789811220326_0007
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引用次数: 0
BACK MATTER 回到问题
An Elementary Overview of Mathematical Structures Pub Date : 2020-08-18 DOI: 10.1142/9789811220326_bmatter
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引用次数: 0
FRONT MATTER 前页
An Elementary Overview of Mathematical Structures Pub Date : 2020-08-18 DOI: 10.1142/9789811220326_fmatter
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引用次数: 0
Topological structures, II 拓扑结构2
An Elementary Overview of Mathematical Structures Pub Date : 2020-08-18 DOI: 10.1142/9789811220326_0005
{"title":"Topological structures, II","authors":"","doi":"10.1142/9789811220326_0005","DOIUrl":"https://doi.org/10.1142/9789811220326_0005","url":null,"abstract":"","PeriodicalId":427744,"journal":{"name":"An Elementary Overview of Mathematical Structures","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132811122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Categories and functors 范畴和函子
An Elementary Overview of Mathematical Structures Pub Date : 2020-08-18 DOI: 10.1007/978-0-387-48101-2_10
S. September
{"title":"Categories and functors","authors":"S. September","doi":"10.1007/978-0-387-48101-2_10","DOIUrl":"https://doi.org/10.1007/978-0-387-48101-2_10","url":null,"abstract":"","PeriodicalId":427744,"journal":{"name":"An Elementary Overview of Mathematical Structures","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131209391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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