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Beyond Topology
 
Edited by: Frédéric Mynard Georgia Southern University, Statesboro, GA
Elliott Pearl , Toronto, ON, Canada
Beyond Topology
Softcover ISBN:  978-0-8218-4279-9
Product Code:  CONM/486
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-8165-1
Product Code:  CONM/486.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4279-9
eBook: ISBN:  978-0-8218-8165-1
Product Code:  CONM/486.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Beyond Topology
Click above image for expanded view
Beyond Topology
Edited by: Frédéric Mynard Georgia Southern University, Statesboro, GA
Elliott Pearl , Toronto, ON, Canada
Softcover ISBN:  978-0-8218-4279-9
Product Code:  CONM/486
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-8165-1
Product Code:  CONM/486.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4279-9
eBook ISBN:  978-0-8218-8165-1
Product Code:  CONM/486.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 4862009; 383 pp
    MSC: Primary 54

    The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.

    Readership

    Graduate students and research mathematicians interested in topology, geometry, analysis, and the foundations of mathematics.

  • Table of Contents
     
     
    • Articles
    • Robert Lowen, Mark Sioen and Stijn Verwulgen — Categorical topology [ MR 2521941 ]
    • H. Lamar Bentley, Eva Colebunders and Eva Vandersmissen — A convenient setting for completions and function spaces [ MR 2521942 ]
    • Anna Di Concilio — Proximity: a powerful tool in extension theory, function spaces, hyperspaces, Boolean algebras and point-free geometry [ MR 2521943 ]
    • Szymon Dolecki — An initiation into convergence theory [ MR 2521944 ]
    • Marcel Erné — Closure [ MR 2521945 ]
    • Hans-Peter A. Künzi — An introduction to quasi-uniform spaces [ MR 2521946 ]
    • Robert Lowen and Christophe Van Olmen — Approach theory [ MR 2521947 ]
    • Gerhard Preuß — Semiuniform convergence spaces and filter spaces [ MR 2521948 ]
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 4862009; 383 pp
MSC: Primary 54

The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.

Readership

Graduate students and research mathematicians interested in topology, geometry, analysis, and the foundations of mathematics.

  • Articles
  • Robert Lowen, Mark Sioen and Stijn Verwulgen — Categorical topology [ MR 2521941 ]
  • H. Lamar Bentley, Eva Colebunders and Eva Vandersmissen — A convenient setting for completions and function spaces [ MR 2521942 ]
  • Anna Di Concilio — Proximity: a powerful tool in extension theory, function spaces, hyperspaces, Boolean algebras and point-free geometry [ MR 2521943 ]
  • Szymon Dolecki — An initiation into convergence theory [ MR 2521944 ]
  • Marcel Erné — Closure [ MR 2521945 ]
  • Hans-Peter A. Künzi — An introduction to quasi-uniform spaces [ MR 2521946 ]
  • Robert Lowen and Christophe Van Olmen — Approach theory [ MR 2521947 ]
  • Gerhard Preuß — Semiuniform convergence spaces and filter spaces [ MR 2521948 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.