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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
🔗Related Documents
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