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Defects of properties in mathematics : quantitative characterizations /
"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; measur...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, NJ :
World Scientific,
©2002.
|
| Colección: | Series on concrete and applicable mathematics ;
v. 5. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Ban, Adrian I. | |
| 245 | 1 | 0 | |a Defects of properties in mathematics : |b quantitative characterizations / |c Adrian I. Ban & Sorin G. Gal. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2002. | ||
| 300 | |a 1 online resource (xi, 352 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Series on concrete and applicable mathematics ; |v v. 5 | |
| 504 | |a Includes bibliographical references (pages 337-348) and index. | ||
| 520 | |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. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |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. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
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| 650 | 0 | |a Fuzzy mathematics. | |
| 650 | 0 | |a Deviation (Mathematics) | |
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| 650 | 6 | |a Mathématiques floues. | |
| 650 | 6 | |a Déviation (Mathématiques) | |
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| 700 | 1 | |a Gal, Sorin G., |d 1953- | |
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| 830 | 0 | |a Series on concrete and applicable mathematics ; |v v. 5. | |
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