Buch, Englisch, Band 7, 261 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g
A Selection of Theorems and Counterexamples
Buch, Englisch, Band 7, 261 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g
Reihe: Atlantis Studies in Mathematics
ISBN: 978-3-030-22234-5
Verlag: Springer International Publishing
Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
- 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. - ?-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. -
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-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. - Fedorcuk’s Resolutions. - Compact Spaces Without Intermediate Dimensions. - More Continua with Distinct Covering and Inductive Dimensions. - The Gaps Between the Dimensions of Normal Hausdorff Spaces.