PDF-Solution.Supposeforacontradictionthatf:M!Misacontractionmappingfromcom
XYX
YSolutionToseeaimpliesbletXandYbetheclosedsetsCandDfromTheorem452iiiNotethattheclosureofaclosedsetisitselfToseebimpliesanotethatsinceMXYandXY
XYwehaveYXcHence
XXc
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