Packet 8: Tossup 17

Injective continuous maps on Euclidean space preserve this property by an “invariance of domain” proved by Brouwer. The Baire property is alternatively named for “almost” having this property up to the difference of a meager set. A countable intersection of sets with this property is a G-delta set. Holomorphic, (-5[2])non-constant functions necessarily have this property, (-5[2])which can be proved using the local degree theorem or Rouche’s theorem. (-5[1])A mapping theorem named for this property (-5[1])generalizes the maximum modulus principle. (10[2]-5[1])By definition, holomorphic functions are complex differentiable (-5[2])at each point on a set with this property. (10[2])For a topological (-5[1])space, a “neighborhood” of a point (-5[1])has this (10[1])property, (10[1]-5[1])which (-5[1])is preserved by finite intersections and arbitrary unions. For 10 points, name this property of intervals not containing (10[1])their endpoints. (10[2])■END■ (10[13]0[2])

Back to tossups

Buzzes

Summary