Defects of properties in mathematics: quantitative characterizations
(eBook)
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Contributors:
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Published:
Singapore ; River Edge, NJ : World Scientific, ©2002.
Format:
eBook
ISBN:
9789812777645, 9812777644, 9789810249243, 9810249241
Physical Desc:
1 online resource (xi, 352 pages)
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Ebsco (CCU)
Description
"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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APA Citation (style guide)
Ban, A. I., & Gal, S. G. (2002). Defects of properties in mathematics: quantitative characterizations. Singapore ; River Edge, NJ, World Scientific.
Chicago / Turabian - Author Date Citation (style guide)Ban, Adrian I and Sorin G. Gal. 2002. Defects of Properties in Mathematics: Quantitative Characterizations. Singapore ; River Edge, NJ, World Scientific.
Chicago / Turabian - Humanities Citation (style guide)Ban, Adrian I and Sorin G. Gal, Defects of Properties in Mathematics: Quantitative Characterizations. Singapore ; River Edge, NJ, World Scientific, 2002.
MLA Citation (style guide)Ban, Adrian I. and Sorin G. Gal. Defects of Properties in Mathematics: Quantitative Characterizations. Singapore ; River Edge, NJ, World Scientific, 2002.
Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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Language:
English
Notes
Bibliography
Includes bibliographical references (pages 337-348) and index.
Description
"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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Grouped Work ID:
70fa5ae4-5d2c-637a-9b9c-1c205d5b59ee
Record Information
| Last File Modification Time | Apr 05, 2024 09:23:17 PM |
|---|---|
| Last Grouped Work Modification Time | Apr 05, 2024 09:12:39 PM |
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| 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) | ||
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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. | |
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