22Axx Topological algebraic systems
This subtopic studies topological algebraic systems, where algebraic operations are considered together with topological structure and continuity requirements.
Specific topics
22A05 Structure of general topological groups
Overview
22A05 studies structure of general topological groups in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for structure of general topological groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks
22A10 Analysis on general topological groups
Overview
22A10 studies analysis on general topological groups in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analysis on general topological groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks
22A15 Structure of topological semigroups
Overview
22A15 studies structure of topological semigroups in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for structure of topological semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks
22A20 Analysis on topological semigroups
Overview
22A20 studies analysis on topological semigroups in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analysis on topological semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks
22A22 Topological groupoids
Overview
22A22 studies topological groupoids in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for topological groupoids
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks
22A25 Representations of general topological groups and semigroups
Overview
22A25 studies representations of general topological groups and semigroups in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of general topological groups and semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks
22A26 Topological semilattices, lattices and applications
Overview
22A26 studies topological semilattices, lattices and applications in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for topological semilattices, lattices and applications
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks
22A30 Other topological algebraic systems and their representations
Overview
22A30 studies other topological algebraic systems and their representations in topological algebraic systems. It studies algebraic systems endowed with compatible topologies, focusing on continuity, representations, and structural properties.
Related Wikipedia Page
Topological Algebraic Systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other topological algebraic systems and their representations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in harmonic analysis, topological dynamics, and the study of continuous algebraic operations.
Applications
- Topological groups and semigroups
- Continuous algebraic representations
- Applications in harmonic analysis
References
Recommended Textbooks