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Continuity (Topological)

★★★★☆Undergraduate

📖Definition

A function f: X → Y between topological spaces is continuous if the preimage of every open set in Y is open in X.

f⁻¹(V) ∈ τ_X for all V ∈ τ_Y

Topological definition of continuity

예제 1

Show that constant functions are continuous.

Generalization of ε-δ continuity

Properties preserved under continuous maps

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