A real function , where is said to be lower semi-continuous in if
and is said to be upper semi-continuous if
A real function is continuous in if and only if it is both upper and lower semicontinuous in .
We can generalize the definition to arbitrary topological spaces as follows.
Let be a topological space. is lower semicontinuous at if, for each there is a neighborhood of such that implies .
|Date of creation||2013-03-22 12:45:41|
|Last modified on||2013-03-22 12:45:41|
|Last modified by||drini (3)|