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021003s2002 si ob 001 0 eng d |
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|a QA39.3
|b .B36 2002eb
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|a MAT
|x 039000
|2 bisacsh
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|a HCDD
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1 |
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|a Ban, Adrian I.
|1 https://id.oclc.org/worldcat/entity/E39PCjCDd7F7btF9rpRKVtb3HC
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| 245 |
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|a Defects of properties in mathematics :
|b quantitative characterizations /
|c Adrian I. Ban & Sorin G. Gal.
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| 260 |
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|a Singapore ;
|a River Edge, NJ :
|b World Scientific,
|c ©2002.
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| 300 |
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|a 1 online resource (xi, 352 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 347 |
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|a data file
|2 rda
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| 490 |
1 |
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|a Series on concrete and applicable mathematics ;
|v v. 5
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| 504 |
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|a Includes bibliographical references (pages 337-348) and index.
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|a "This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--Page 2 of cover.
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|a Print version record.
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|a Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems.
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| 650 |
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|a Mathematics.
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| 650 |
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|a Fuzzy mathematics.
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| 650 |
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|a Deviation (Mathematics)
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| 650 |
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|a applied mathematics.
|2 aat
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| 650 |
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|a mathematics.
|2 aat
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| 650 |
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|a MATHEMATICS
|x Essays.
|2 bisacsh
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| 650 |
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|a MATHEMATICS
|x Pre-Calculus.
|2 bisacsh
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| 650 |
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|a MATHEMATICS
|x Reference.
|2 bisacsh
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| 650 |
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|a Deviation (Mathematics)
|2 fast
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| 650 |
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|a Fuzzy mathematics
|2 fast
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| 650 |
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|a Mathematics
|2 fast
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| 700 |
1 |
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|a Gal, Sorin G.,
|d 1953-
|1 https://id.oclc.org/worldcat/entity/E39PCjxmpxDQH799yTC9rc6R8C
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| 758 |
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|i has work:
|a Defects of properties in mathematics (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCGkB8CqK33xwF7r8Bfb7h3
|4 https://id.oclc.org/worldcat/ontology/hasWork
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| 776 |
0 |
8 |
|i Print version:
|a Ban, Adrian I.
|t Defects of properties in mathematics.
|d Singapore ; River Edge, NJ : World Scientific, ©2002
|z 9810249241
|z 9789810249243
|w (DLC) 2002514305
|w (OCoLC)50033967
|
| 830 |
|
0 |
|a Series on concrete and applicable mathematics ;
|v v. 5.
|
| 856 |
4 |
0 |
|u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=1679535
|y Click for online access
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|a EBC-AC
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|a 92
|b HCD
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