Brouwer fixed-point theorem: Difference between revisions

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==Importance of the pre-conditions==
The theorem holds only for functions that are ''endomorphisms'' (functions that have the same set as the ___domain and rangecodomain) and for sets that are ''compact'' (thus, in particular, bounded and closed) and ''convex'' (or [[Homeomorphism|homeomorphic]] to convex). The following examples show why the pre-conditions are important.
 
===The function ''f'' as an endomorphism===