UID:
almahu_9947367964802882
Format:
1 online resource (347 p.)
ISBN:
1-281-77896-6
,
9786611778965
,
0-08-088761-9
Series Statement:
North-Holland mathematical library ; v. 48
Content:
Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a s
Note:
Description based upon print version of record.
,
Front Cover; Dimension and Extensions; Copyright Page; Contents; Preface; Chapter I. The separable case in historical perspective; I.1. A compactification problem; I.2. Dimensionsgrad; I.3. The small inductive dimension ind; I.4. The large inductive dimension Ind; I.5. The compactness degree; de Groot's problem; I.6. Splitting the compactification problem; I.7. The completeness degree; I.8. The covering dimension dim; I.9. The covering completeness degree; I.10. The s-compactness degree; I.11. Pol's example; I.12. Kimura's theorem; I.13. Guide to dimension theory
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I.14. Historical comments and unsolved problemsChapter II. Mappings into spheres; II.1. Classes and universe; II.2. Inductive dimension modulo a class P; II.3. Kernels and surplus; II.4. P-Ind and mappings into spheres; II.5. Covering dimensions modulo a class P; II.6. P-dim and mappings into spheres; II.7. Comparison of P-Ind and P-dim; II.8. Hulls and deficiency; II.9. Absolute Borel classes in metric spaces; II.10. Dimension modulo Borel classes; II.11. Historical comments and unsolved problems; Chapter III. Functions of inductive dimensional type; III.1. Additivity; III.2. Normal families
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III.3. Optimal universeIII.4. Embedding theorems; III.5. Axioms for the dimension function; III.6. Historical comments and unsolved problems; Chapter IV. Functions of covering dimensional type; IV.1. Finite unions; IV.2. Normal families; IV.3. The Dowker universe D; IV.4. Dimension and mappings; IV.5. Historical comments and unsolved problems; Chapter V. Functions of basic dimensional type; V.1. The basic inductive dimension; V.2. Excision and extension; V.3. The order dimension; V.4. The mixed inductive dimension; V.5. Historical comments and unsolved problems; Chapter VI. Compactifications
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VI.l. Wallman compactificationsVI.2. Dimension preserving compactifications; VI.3. The Fkeudenthal compactification; VI.4. The inequality K-Ind = K-Def; VI.5. Kimura's characterization of K-def; VI.6. The inequality K-dim = K-def; VI.7. Historical comments and unsolved problems; Chart 1. The absolute Borel classes; Chart 2. Compactness dimension functions; Bibliography; List of symbols; Index
,
English
Additional Edition:
ISBN 0-444-89740-2
Language:
English
