Category Archives: Algebraic Topology

Wild Embeddings

Yesterday in a discussion in Komero we concluded that if f is an injective (one-to-one) map from the unit interval [0,1] to the Euclidean plane (or [tex]\mathbb{R}^n[/tex]), then the interval is homeomorphic with its image. The proof is as follows: … Continue reading

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Ambient Isotopy

Note: One is able to do puzzles 2 and 3 without reading or understanding the text before them. In knot theory, people define equivalence of knots using the concept of ambient isotopy. Two knots (embeddings of the unit circle into … Continue reading

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