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Dimension Theory

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Cover of 'Dimension Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Topological Spaces
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    Chapter 2 The Three Main Dimension Functions
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    Chapter 3 The Countable Sum Theorem for Covering Dimension
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    Chapter 4 Urysohn Inequalities
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    Chapter 5 The Dimension of Euclidean Spaces
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    Chapter 6 Connected Components and Dimension
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    Chapter 7 Factorization and Compactification Theorems for Separable Metric Spaces
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    Chapter 8 Coincidence, Product and Decomposition Theorems for Separable Metric Spaces
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    Chapter 9 Universal Spaces for Separable Metric Spaces of Dimension at Most n
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    Chapter 10 Axiomatic Characterization of the Dimension of Separable Metric Spaces
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    Chapter 11 Cozero Sets and Covering Dimension dim 0
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    Chapter 12 ψ -Spaces and the Failure of the Sum and Subset Theorems for dim 0
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    Chapter 13 The Inductive Dimension Ind 0
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    Chapter 14 Two Classical Examples
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    Chapter 15 The Gap Between the Covering and the Inductive Dimensions of Compact Hausdorff Spaces
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    Chapter 16 Inverse Limits and N -Compact Spaces
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    Chapter 17 Some Standard Results Concerning Metric Spaces
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    Chapter 18 The Mardešić Factorization Theorem and the Dimension of Metrizable Spaces
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    Chapter 19 A Metrizable Space with Unequal Inductive Dimensions
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    Chapter 20 No Finite Sum Theorem for the Small Inductive Dimension of Metrizable Spaces
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    Chapter 21 Failure of the Subset Theorem for Hereditarily Normal Spaces
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    Chapter 22 A Zero-Dimensional, Hereditarily Normal and Lindelöf Space Containing Subspaces of Arbitrarily Large Dimension
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    Chapter 23 Cosmic Spaces and Dimension
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    Chapter 24 n -Cardinality and Bernstein Sets
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    Chapter 25 The van Douwen Technique for Constructing Counterexamples
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    Chapter 26 No Compactification Theorem for the Small Inductive Dimension of Perfectly Normal Spaces
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    Chapter 27 Normal Products and Dimension
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    Chapter 28 Fully Closed and Ring-Like Maps
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    Chapter 29 Fedorčuk’s Resolutions
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    Chapter 30 Compact Spaces Without Intermediate Dimensions
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    Chapter 31 More Continua with Distinct Covering and Inductive Dimensions
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    Chapter 32 The Gaps Between the Dimensions of Normal Hausdorff Spaces
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Title
Dimension Theory
Published by
Springer International Publishing, October 2019
DOI 10.1007/978-3-030-22232-1
ISBNs
978-3-03-022231-4, 978-3-03-022232-1
Authors

Charalambous, Michael G.

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