Dimension Theory

- Topological Spaces. - The Three Main Dimension Functions. - The Countable Sum Theorem for Covering Dimension. - Urysohn Inequalities. - The Dimension of Euclidean Spaces. - Connected Components and Dimension. - Factorization and Compactification Theorems for Separable Metric Spaces. - Coincidence, Product and Decomposition Theorems for Separable Metric Spaces. - Universal Spaces for Separable Metric Spaces of Dimension at Most n. - Axiomatic Characterization of the Dimension of Separable Metric Spaces. - Cozero Sets and Covering Dimension dim0. - ψ-Spaces and the Failure of the Sum and Subset Theorems for dim0. - The Inductive Dimension Ind0. - Two Classical Examples. - The Gap Between the Covering and the Inductive Dimensions of Compact Hausdorff Spaces. - Inverse Limits and N-Compact Spaces. - Some Standard Results Concerning Metric Spaces. - The Mardeši´c Factorization Theorem and the Dimension of Metrizable Spaces. - A Metrizable Space with Unequal Inductive Dimensions. - No Finite Sum Theorem for the Small Inductive Dimension of Metrizable Spaces. - Failure of the Subset Theorem for Hereditarily Normal Spaces. - A Zero-Dimensional, Hereditarily Normal and Lindelöf Space Containing Subspaces of Arbitrarily Large Dimension. - Cosmic Spaces and Dimension. - n-Cardinality and Bernstein Sets. - The van Douwen Technique for Constructing Counterexamples. - No Compactification Theorem for the Small Inductive Dimension of Perfectly Normal Spaces. - Normal Products and Dimension. - Fully Closed and Ring-Like Maps. - Fedorčuk’s Resolutions. - Compact Spaces Without Intermediate Dimensions. - More Continua with Distinct Covering and Inductive Dimensions. - The Gaps Between the Dimensions of Normal Hausdorff Spaces.