Description 
1 online resource (xi, 352 pages) 
Series 
Series on concrete and applicable mathematics ; v. 5 

Series on concrete and applicable mathematics ; v. 5

Contents 
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 
Summary 
"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 
Bibliography 
Includes bibliographical references (pages 337348) and index 
Notes 
Print version record 
Subject 
Deviation (Mathematics)


Fuzzy mathematics.


Mathematics.

Form 
Electronic book

Author 
Gal, Sorin G., 1953

ISBN 
9789810249243 

9789812777645 (electronic bk.) 

9810249241 

9812777644 (electronic bk.) 
