Examples. Of course every homeomorphism is a local homeomorphism, but the converse is not true. For example, let be an exponential function, i.e. . Then is a local homeomorphism, but it is not a homeorphism (indeed, for any ).
One of the most important theorem of differential calculus (i.e. inverse function theorem) states, that if is a -map between -manifolds such that is a linear isomorphism for a given , then is locally invertible in (in this case the local inverse is even a -map).
|Date of creation||2013-03-22 18:53:47|
|Last modified on||2013-03-22 18:53:47|
|Last modified by||joking (16130)|