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This subtopic introduces the core ideas in maps and general topological 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.
Continuous maps in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Weak and generalized continuity in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Special maps on topological spaces (open, closed, etc.). This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Retraction in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Extension of maps in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Embedding of topological spaces. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Real-valued functions in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Function spaces in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Algebraic properties of function spaces in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
$C$- and $C^*$-embedding in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Special sets defined by functions in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract, absolute retract spaces. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Shape theory in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Set-valued maps in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Selections in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.
Entropy in general topology. This topic analyzes continuous maps and general morphisms between topological spaces, emphasizing structural and categorical behavior.
Wikipedia: Continuous function
Used to classify spaces and transformations through map properties and invariants.