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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 |
Tabla de Contenidos:
- 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.