For T a topological space and X a real normed space S(T,X) denotes the set of continuous mappings from T into S(X) = {x implied by X:||x|| = 1}. Given f in S(T,X) we study the existence of functions e in S(T,X) such that f(t) not= e(t) not= -f(t), t implied by T. When this holds for every f, we say that S(T,X) is plentiful. If dim X is an even integer or infinite this last property is automatic for any T. We show that it also verifies if T is a contractible compact space and X is an arbitrary normed space with dim X >=2. From this we deduce that if T is completely regular and dim T 展开▼
机译：对于T，拓扑空间和X的实数范数空间S（T，X）表示从T到S（X）= {x的X：|| x ||隐含的连续映射集。 = 1}。给定S（T，X）中的f，我们研究S（T，X）中函数e的存在，使得f（t）不等于e（t）不等于-f（t），t表示T。对于每个f成立，我们说S（T，X）足够。如果dim X是偶数整数或无穷大，则最后一个属性对于任何T都是自动的。我们证明了它还可以验证T是否是可压缩的紧致空间，并且X是Dimm X> = 2的任意范数空间。由此推论出，如果T是完全规则的且Dim T 展开▼
