The Resource Index Analysis : Approach Theory at Work, by R. Lowen, (electronic resource)
Index Analysis : Approach Theory at Work, by R. Lowen, (electronic resource)
Resource Information
The item Index Analysis : Approach Theory at Work, by R. Lowen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Index Analysis : Approach Theory at Work, by R. Lowen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 A featured review of the AMS describes the author's earlier work in the field of approach spaces as, ‘A landmark in the history of general topology'. In this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis. Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science
 Language
 eng
 Extent
 XXI, 466 p. 58 illus.
 Contents

 Approach spaces
 Topological and metric approach spaces
 Approach invariants
 Index analysis
 Uniform gauge spaces
 Extensions of spaces and morphisms
 Approach theory meets Topology
 Approach theory meets Functional analysis
 Approach theory meets Probability
 Approach theory meets Hyperspaces
 Approach theory meets DCPO's and Domains
 Categorical considerations
 Isbn
 9781447164852
 Label
 Index Analysis : Approach Theory at Work
 Title
 Index Analysis
 Title remainder
 Approach Theory at Work
 Statement of responsibility
 by R. Lowen
 Language
 eng
 Summary
 A featured review of the AMS describes the author's earlier work in the field of approach spaces as, ‘A landmark in the history of general topology'. In this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis. Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science
 http://library.link/vocab/creatorName
 Lowen, R
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Ordered algebraic structures
 Approximation theory
 Functional analysis
 Geometry
 Probabilities
 Topology
 Label
 Index Analysis : Approach Theory at Work, by R. Lowen, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Approach spaces  Topological and metric approach spaces  Approach invariants  Index analysis  Uniform gauge spaces  Extensions of spaces and morphisms  Approach theory meets Topology  Approach theory meets Functional analysis  Approach theory meets Probability  Approach theory meets Hyperspaces  Approach theory meets DCPO's and Domains  Categorical considerations
 Control code
 9781447164852
 Dimensions
 unknown
 Extent
 XXI, 466 p. 58 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781447164852
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9781447164852
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086469764
 Label
 Index Analysis : Approach Theory at Work, by R. Lowen, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Approach spaces  Topological and metric approach spaces  Approach invariants  Index analysis  Uniform gauge spaces  Extensions of spaces and morphisms  Approach theory meets Topology  Approach theory meets Functional analysis  Approach theory meets Probability  Approach theory meets Hyperspaces  Approach theory meets DCPO's and Domains  Categorical considerations
 Control code
 9781447164852
 Dimensions
 unknown
 Extent
 XXI, 466 p. 58 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781447164852
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9781447164852
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086469764
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/IndexAnalysisApproachTheoryatWorkbyR./Ao8vKGByiH0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/IndexAnalysisApproachTheoryatWorkbyR./Ao8vKGByiH0/">Index Analysis : Approach Theory at Work, by R. Lowen, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>