52Axx Convex sets in linear spaces
This subtopic introduces the core ideas in convex sets in linear spaces, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
52A01 Axiomatic and generalized convexity
Overview
Axiomatic and generalized convexity. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A05 Convex sets without dimension restrictions
Overview
Convex sets without dimension restrictions. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A07 Convex sets in topological vector spaces
Overview
Convex sets in topological vector spaces. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A10 Convex sets in $2$ dimensions
Overview
Convex sets in $2$ dimensions. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A15 Convex sets in $3$ dimensions
Overview
Convex sets in $3$ dimensions. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A20 Convex sets in $n$ dimensions
Overview
Convex sets in $n$ dimensions. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A21 Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.)
Overview
Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.). This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A22 Random convex sets and integral geometry
Overview
Random convex sets and integral geometry. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A23 Asymptotic theory of convex bodies
Overview
Asymptotic theory of convex bodies. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A27 Approximation by convex sets
Overview
Approximation by convex sets. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A30 Variants of convex sets (star-shaped, $(m,n)$-convex, etc.)
Overview
Variants of convex sets (star-shaped, $(m,n)$-convex, etc.). This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A35 Helly-type theorems and geometric transversal theory
Overview
Helly-type theorems and geometric transversal theory. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A37 Other problems of combinatorial convexity
Overview
Other problems of combinatorial convexity. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A38 Length, area, volume and convex sets
Overview
Length, area, volume and convex sets. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A39 Mixed volumes and related topics in convex geometry
Overview
Mixed volumes and related topics in convex geometry. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A40 Inequalities and extremum problems involving convexity in convex geometry
Overview
Inequalities and extremum problems involving convexity in convex geometry. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A41 Convex functions and convex programs in convex geometry
Overview
Convex functions and convex programs in convex geometry. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks
52A55 Spherical and hyperbolic convexity
Overview
Spherical and hyperbolic convexity. This topic studies convex sets in linear spaces with emphasis on structure, extremal properties, and geometric inequalities.
Related Wikipedia Page
Wikipedia: Convex set
Useful Links
Key Ideas
- convexity in linear spaces
- extreme points and supporting structures
- dimension-dependent and dimension-free methods
Typical Uses
Used to model optimization domains, geometric inequalities, and structural properties of high-dimensional bodies.
Applications
- Optimization theory
- Functional analysis
- Computational geometry
References
Recommended Textbooks