According to Hawking and Ellis: "A manifold is a space locally similar to Euclidean space in that it can be covered by coordinate patches. This structure allows differentiation to be defined, but does not distinguish between different coordinate systems. Thus, the only concepts defined by the manifold structure are those that are independent of the choice of a coordinate system." Stephen W. Hawking & George Francis Rayner Ellis. The Large Scale Structure of Space-Time. Cambridge University Press. 1973: 11 [2013-02-08]. ISBN 0-521-09906-4. （原始内容存档于2017-01-07）. A mathematical definition is: A connected Hausdorff spaceM is called an n-dimensional manifold if each point of M is contained in an open set that is homeomorphic to an open set in Euclidean n-dimensional space.
According to Hawking and Ellis: "A manifold is a space locally similar to Euclidean space in that it can be covered by coordinate patches. This structure allows differentiation to be defined, but does not distinguish between different coordinate systems. Thus, the only concepts defined by the manifold structure are those that are independent of the choice of a coordinate system." Stephen W. Hawking & George Francis Rayner Ellis. The Large Scale Structure of Space-Time. Cambridge University Press. 1973: 11 [2013-02-08]. ISBN 0-521-09906-4. （原始内容存档于2017-01-07）. A mathematical definition is: A connected Hausdorff spaceM is called an n-dimensional manifold if each point of M is contained in an open set that is homeomorphic to an open set in Euclidean n-dimensional space.
