Brouwer Fixed-Point Theorem

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Brouwer Fixed-Point Theorem

(topology)
A well-known result in topology stating that any continuous transformation of an n-dimensional disk must have at least one fixed point.

References in periodicals archive ?
PARK, VJM 27 (1999) [31]--This historical article is to survey the developments of the fields of mathematics directly related to the nearly ninety-year-old Brouwer fixed point theorem. We are mainly concerned with equivalent formulations and generalizations of the theorem.
Hence, applying Brouwer fixed point theorem to the operator f[(m).sup.1/[sigma]] (see, e.g., [18]), we see that the operator has a fixed point in L([w.bar],[bar.w]).
By the Brouwer fixed point theorem, there is at least one fixed point of [F.sup.[alpha]], that is, zero point of (1) in [[OMEGA].sup.[alpha]].