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Homeomorphism

★★★★☆Undergraduate

📖Definition

A homeomorphism is a continuous bijection with a continuous inverse. Homeomorphic spaces are topologically identical.

📐Formulas

f: X → Y homeomorphism ⇔ f, f⁻¹ continuous bijection

Definition of homeomorphism

✏️Examples

예제 1

Explain why a sphere and cube are homeomorphic.

예제 2

Explain why a circle and line are not homeomorphic.

Applications

Classification

Classification of spaces

Physics

Phase transitions, topological defects

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#위상동형#연속#homeomorphism#topology