In the area of mathematics known as differential topology, the disc theorem of Palais (1960) states that two embeddings of a closed k-disc into a connected n-manifold are ambient isotopic provided that if k = n the two embeddings are equioriented. The disc theorem implies that the connected sum of smooth oriented manifolds is well defined. A different although related and similar named result is the disc embedding theorem proved by Freedman in 1982.
References
Sources Palais, Richard S. (1960), "Extending diffeomorphisms", Proceedings of the American Mathematical Society, 11: 274–277, doi:10.2307/2032968, ISSN 0002-9939, JSTOR 2032968, MR 0117741