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Defects of properties in mathematics : quantitative characterizations

Author: Adrian I Ban; Sorin G Gal
Publisher: Singapore ; River Edge, NJ : World Scientific, ©2002.
Series: Series on concrete and applicable mathematics, v. 5.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ban, Adrian I.
Defects of properties in mathematics.
Singapore ; River Edge, NJ : World Scientific, ©2002
(DLC) 2002514305
(OCoLC)50033967
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Adrian I Ban; Sorin G Gal
ISBN: 9789812777645 9812777644 9789810249243 9810249241
OCLC Number: 614463596
Description: 1 online resource (xi, 352 pages).
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.
Series Title: Series on concrete and applicable mathematics, v. 5.
Responsibility: Adrian I. Ban & Sorin G. Gal.

Abstract:

An introduction to 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)  Read more...

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