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Spectral Spaces Max Dickmann 1st Edition by Max Dickmann, Niels Schwartz, Marcus Tressl ISBN 1107146720 9781107146723

Name: Spectral Spaces Max Dickmann 1st Edition by Max Dickmann, Niels Schwartz, Marcus Tressl ISBN 1107146720 9781107146723
SKU: EB-9958210
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Spectral Spaces Max Dickmann Digital Instant Download

Author(s): Max Dickmann; Niels Schwartz; Marcus Tressl

ISBN(s): 9781107146723, 1107146720

Edition: Hardcover

File Details: PDF, 3.09 MB

Year: 2019

Language: English

SKU: EB-9958210 Category: Mathematics Tags: Marcus Tressl, Max Dickmann, Niels Schwartz

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Spectral Spaces Max Dickmann 1st Edition by Max Dickmann, Niels Schwartz, Marcus Tressl – Ebook PDF Instant Download/Delivery: 1107146720 ,9781107146723
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Product details:
ISBN 10: 1107146720
ISBN 13: 9781107146723
Author: Max Dickmann, Niels Schwartz, Marcus Tressl

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Spectral Spaces Max Dickmann 1st Edition Table of contents:

Introduction
- Overview of spectral spaces
- Applications in functional analysis, algebraic geometry, and topology
- Motivation and objectives of the book
Preliminaries
- Topological spaces and basic concepts
- Review of spectral theory
- Categories and functors in algebraic geometry
- Spectral spaces and their properties
Spectral Spaces: Definitions and Basic Properties
- Definition of spectral spaces
- Examples and key properties
- Comparison with other types of spaces (e.g., sober spaces)
- Topological and algebraic structure
Spectral Topology and Compactness
- Compact spectral spaces
- Topological properties of spectral spaces
- Spectral compactness and applications
- Continuous functions on spectral spaces
Algebraic Aspects of Spectral Spaces
- Spectral spaces as spectra of commutative rings
- Connections to algebraic geometry
- Spectral theory of commutative algebras
- Structure of algebras over spectral spaces
Sheaf Theory and Cech Cohomology
- Introduction to sheaf theory
- Cech cohomology of spectral spaces
- Applications to spectral spaces and their algebraic structure
The Spectrum of a Space
- The spectrum of a topological space
- Topological spectra in functional analysis
- Spectral spaces as spectra of topological algebras
- Sheaves and spectral spaces
Spectral Spaces and C-Algebras*
- Relation between spectral spaces and C*-algebras
- Applications to operator theory
- Spectral representation theorems
- Spectral spaces in quantum mechanics and functional analysis
Applications to Algebraic Geometry
- Spectral spaces and their role in algebraic geometry
- Spectral spaces as spaces of prime ideals
- Connections to affine and projective varieties
- Spectral spaces in the context of schemes and spectra
Advanced Topics in Spectral Theory
- Non-commutative spectral theory
- Advanced methods in spectral space theory
- Homotopy and spectral spaces
- Spectral spaces in higher dimensions
Case Studies and Examples
- Worked examples of spectral spaces in algebraic geometry
- Spectral spaces in the theory of dynamical systems
- Computational methods for studying spectral spaces
Concluding Remarks and Open Problems
- Summary of results
- Open questions in spectral space theory
- Future directions for research
Appendices
- Mathematical prerequisites and further reading
- Notation and conventions
- Additional resources and references