Editing Geometric topology (section)

===Schönflies theorems===
{{main|Jordan-Schönflies theorem}}
The generalized [[Schoenflies theorem]] states that, if an (''n''&nbsp;&minus;&nbsp;1)-dimensional [[sphere]] ''S'' is embedded into the ''n''-dimensional sphere ''S<sup>n</sup>'' in a [[locally flat]] way (that is, the embedding extends to that of a thickened sphere), then the pair (''S<sup>n</sup>'',&nbsp;''S'') is homeomorphic to the pair (''S<sup>n</sup>'', ''S''<sup>''n''&minus;1</sup>), where ''S''<sup>''n''&minus;1</sup> is the equator of the ''n''-sphere.  Brown and Mazur received the [[Veblen Prize]] for their independent proofs<ref>[[Morton Brown|Brown, Morton]] (1960), A proof of the generalized Schoenflies theorem. ''Bull. Amer. Math. Soc.'', vol. 66, pp.&nbsp;74&ndash;76. {{MR|0117695}}</ref><ref>Mazur, Barry, On embeddings of spheres., ''Bull. Amer. Math. Soc.'' 65 1959 59&ndash;65. {{MR|0117693}}
</ref> of this theorem.