广义度量空间与映射
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作者林寿，恽自求
出版社科学出版社
ISBN9787030522214
出版时间2017-04
装帧平装
开本其他
定价128元
货号25064984
上书时间2024-10-27
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前言
序言
目录
Foreword
Preface
Preface to the English Edition
Chapter 1 The origin of generalized metric spaces
1,1 Notations and terminologies
1.2 Distance functions
1.3 Bases
1.4 Stratifications
1.5 Networks and (rood k)-networks
1.6 k-networks and weak bases
1.7 Generalized countably compact spaces
1.8 Examples
Chapter 2 Mappings on metric spaces
2.1 Classes of mappings
2.2 Perfect mappings
2.3 Quotient mappings
2.4 Open mappings
2.5 Closed mappings
2.6 Compact-covering mappings
2.7 s-mappings
2.8 ss-mappings
2.9 7r-mappings
2.10 Compact mappings
2.11 a-locally finite mappings
Chapter 3 Generalized metric spaces
3.1 Spaces with point-countable covers
3.2 Z-spaces
3.3 a-spaces and semi-stratifiable spaces
3.4 k-semi-stratifiable spaces
3.5 Mi-spaces
3.6 Developable spaces and p-spaces
3.7 M-spaces
3.8 R-spaces
3.9 g-metrizable spaces
3.10 Open questions
Appendix A Characterizations of several covering properties
A.1 Paracompact spaces
A.2 Metacompact spaces
A.3 Subparacompact spaces
A.4 Submetacompact spaces
A.5 Meta-LindelSf spaces
Appendix B The formation of the theory of generalized metric spaces
B.1 A historical review
B.2 The foundation laying period
B.3 The formation period
Bibliography
Index
Mathematics Monograph Series
内容摘要
林寿、恽自求主编的《广义度量空间与映射(英文版)(精)》介绍了，Thisisthefirstbookongeneralizedmetricspaces.Theideasandproblemsofthetheoryofgeneralizedmetricspacesgreatlyinfluencedalldomainsofset-theoretictopology.Amaingoalofthisbookistodescribethepresentstructureofthetheoryofgeneralizedmetricspacesandthemodemdevelopmentsinthistheory.Thebookdiscussesthebasictheoryofgeneralizedmetricspacesbyusingthemappingmethod,andsummarizestheimportantresearchachievementssincethe1960'sparticularlybyChinesescholars.Therearethreechapters“TheOriginofGeneralizedMetricSpaces”,“Map-pingsonMetricSpaces”,and“ClassesofGeneralizedMetricSpaces”.InadditiontherearetwoappendicesofaboutXXpagesintotal,andabout500references.Thebookwillbeavaluablesourceofinformationforgraduateandundergradu-atetopologystudentswishingtoknowmoreaboutthisexcitingfield,orwaysitcouldbeappliedtoothermathematicaldisciplines.Itwillalsobeveryhelpfultoexpertsintopologyalreadyworkingingeneralizedmetricspaces.
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