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▼