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Non-Hausdorff Topology and Domain Theory : Selected Topics in Point-Set Topology.
Introduces the basic concepts of topology with an emphasis on non-Hausdorff topology, which is crucial for theoretical computer science.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Cambridge University Press,
2013.
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| Colección: | New mathematical monographs.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Contents; 1 Introduction; 2 Elements of set theory; 2.1 Foundations; 2.2 Finiteness, countability; 2.3 Order theory; 2.4 The Axiom of Choice; 3 A first tour of topology: metric spaces; 3.1 Metric spaces; 3.2 Convergence, limits; 3.3 Compact subsets; 3.4 Complete metric spaces; 3.5 Continuous functions; 4 Topology; 4.1 Topology, topological spaces; 4.2 Order and topology; 4.3 Continuity; 4.4 Compactness; 4.5 Products; 4.6 Coproducts; 4.7 Convergence and limits; 4.8 Local compactness; 4.9 Subspaces; 4.10 Homeomorphisms, embeddings, quotients, retracts; 4.11 Connectedness.
- 4.12 A bit of category theory I5 Approximation and function spaces; 5.1 The way-below relation; 5.2 The lattice of open subsets of a space; 5.3 Spaces of continuous maps; 5.4 The exponential topology; 5.5 A bit of category theory II; 5.6 C-Generated spaces; 5.7 bc-domains; 6 Metrics, quasi-metrics, hemi-metrics; 6.1 Metrics, hemi-metrics, and open balls; 6.2 Continuous and Lipschitz maps; 6.3 Topological equivalence, hemi-metrizability, metrizability; 6.4 Coproducts, quotients; 6.5 Products, subspaces; 6.6 Function spaces; 6.7 Compactness and symcompactness; 7 Completeness.
- 7.1 Limits, d-limits, and Cauchy nets7.2 A strong form of completeness: Smyth-completeness; 7.3 Formal balls; 7.4 A weak form of completeness: Yoneda-completeness; 7.5 The formal ball completion; 7.6 Choquet-completeness; 7.7 Polish spaces; 8 Sober spaces; 8.1 Frames and Stone duality; 8.2 Sober spaces and sobrification; 8.3 The Hofmann
- Mislove Theorem; 8.4 Colimits and limits of sober spaces; 9 Stably compact spaces and compact pospaces; 9.1 Stably locally compact spaces, stably compact spaces; 9.2 Coproducts and retracts of stably compact spaces.
- 9.3 Products and subspaces of stably compact spaces9.4 Patch-continuous, perfect maps; 9.5 Spectral spaces; 9.6 Bifinite domains; 9.7 Noetherian spaces; References; Notation index; Index.