54Bxx Basic constructions
This subtopic introduces the core ideas in basic constructions, 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
54B05 Subspaces in general topology
Overview
Subspaces in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks
54B10 Product spaces in general topology
Overview
Product spaces in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks
54B15 Quotient spaces, decompositions in general topology
Overview
Quotient spaces, decompositions in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks
54B17 Adjunction spaces and similar constructions in general topology
Overview
Adjunction spaces and similar constructions in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks
54B20 Hyperspaces in general topology
Overview
Hyperspaces in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks
54B30 Categorical methods in general topology
Overview
Categorical methods in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks
54B35 Spectra in general topology
Overview
Spectra in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks
54B40 Presheaves and sheaves in general topology
Overview
Presheaves and sheaves in general topology. This topic studies foundational constructions in topology, including products, quotients, and related operations that build new spaces from old ones.
Related Wikipedia Page
Wikipedia: Topological space
Useful Links
Key Ideas
- product and quotient constructions
- subspace and sum operations
- universal topological constructions
Typical Uses
Used to create and compare spaces in abstract topology and related geometric settings.
Applications
- Algebraic topology foundations
- Functional analysis setups
- Category-theoretic topology
References
Recommended Textbooks