General Topology I: Basic Concepts and Constructions Dimension Theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1990
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
17 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | General topology is the domain ofmathematics devoted to the investigation of the concepts of continuity and passage to a limit at their natural level of generality. The most basic concepts of general topology, that of a topological space and a continuous map, were introduced by Hausdorffin 1914. Oneofthecentralproblemsoftopologyisthedeterminationandinvestigation of topological invariants; that is, properties ofspaces which are preserved under homeomorphisms. Topological invariants need not be numbers. Connectedness, compactness, andmetrizability,forexample,arenon-numericaltopologicalinvariants.Dimen sional invariants, on the otherhand, areexamplesofnumericalinvariants which take integervalues on specific topological spaces. Part II ofthis book is devoted to them. Topological invariants which take values in the cardinal numbers play an especially important role, providing the raw material for many useful coin" putations. Weight, density, character, and Suslin number are invariants ofthis type. Certain classes of topological spaces are defined in terms of topological in variants. Particularly important examples include the metrizable spaces, spaces with a countable base, compact spaces, Tikhonov spaces, Polish spaces, Cech complete spaces and the symmetrizable spaces |
| Beschreibung: | 1 Online-Ressource (VII, 202p. 15 illus) |
| ISBN: | 9783642612657 9783642647673 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-642-61265-7 |
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Datensatz im Suchindex
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| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-61265-7 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642612657 9783642647673 |
| issn | 0938-0396 |
| language | English |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Arkhangel’skii, A. V. Verfasser aut General Topology I Basic Concepts and Constructions Dimension Theory edited by A. V. Arkhangel’skii, L. S. Pontryagin Berlin, Heidelberg Springer Berlin Heidelberg 1990 1 Online-Ressource (VII, 202p. 15 illus) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 17 0938-0396 General topology is the domain ofmathematics devoted to the investigation of the concepts of continuity and passage to a limit at their natural level of generality. The most basic concepts of general topology, that of a topological space and a continuous map, were introduced by Hausdorffin 1914. Oneofthecentralproblemsoftopologyisthedeterminationandinvestigation of topological invariants; that is, properties ofspaces which are preserved under homeomorphisms. Topological invariants need not be numbers. Connectedness, compactness, andmetrizability,forexample,arenon-numericaltopologicalinvariants.Dimen sional invariants, on the otherhand, areexamplesofnumericalinvariants which take integervalues on specific topological spaces. Part II ofthis book is devoted to them. Topological invariants which take values in the cardinal numbers play an especially important role, providing the raw material for many useful coin" putations. Weight, density, character, and Suslin number are invariants ofthis type. Certain classes of topological spaces are defined in terms of topological in variants. Particularly important examples include the metrizable spaces, spaces with a countable base, compact spaces, Tikhonov spaces, Polish spaces, Cech complete spaces and the symmetrizable spaces Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik Pontryagin, L. S. Sonstige oth https://doi.org/10.1007/978-3-642-61265-7 Verlag Volltext |
| spellingShingle | Arkhangel’skii, A. V. General Topology I Basic Concepts and Constructions Dimension Theory Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik |
| title | General Topology I Basic Concepts and Constructions Dimension Theory |
| title_auth | General Topology I Basic Concepts and Constructions Dimension Theory |
| title_exact_search | General Topology I Basic Concepts and Constructions Dimension Theory |
| title_full | General Topology I Basic Concepts and Constructions Dimension Theory edited by A. V. Arkhangel’skii, L. S. Pontryagin |
| title_fullStr | General Topology I Basic Concepts and Constructions Dimension Theory edited by A. V. Arkhangel’skii, L. S. Pontryagin |
| title_full_unstemmed | General Topology I Basic Concepts and Constructions Dimension Theory edited by A. V. Arkhangel’skii, L. S. Pontryagin |
| title_short | General Topology I |
| title_sort | general topology i basic concepts and constructions dimension theory |
| title_sub | Basic Concepts and Constructions Dimension Theory |
| topic | Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik |
| url | https://doi.org/10.1007/978-3-642-61265-7 |
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