论文标题
连续选择，质数和覆盖类型属性
Continuous selections, prime number and a covering type property
论文作者
论文摘要
令$（x，τ）$为hausdorff空间，$ n \inΩ$。我们证明，如果$ x $承认在$ \ mathcal {f} _ {n}（x）$（最多$ n $的$ x $ of $ x $）的$ \ mathcal {f} _ {f} _ {f} _ {f} _ {n}（x）$）中，那么，对于每一个$ n \ leq m \ leq m \ leq m \ leq m \ leq 2n $ $ m $）。因此，当且仅当每个质数相同时，一个空间$ x $就可以对每个自然数字进行连续选择。对于Hausdorff Spaces $（x，τ）$，在$ [x]^2 $上接收连续选择，我们表征了$ [x]^n $在$ n \ geq 2 $上的连续选择，就覆盖型属性而言。
Let $(X,τ)$ be a Hausdorff space and $n\inω$. We prove that if $X$ admits a continuous selection over $\mathcal{F}_{n}(X)$ (nonempty subsets of $X$ of cardinality at most $n$), then for every $n\leq m\leq 2n$ such that $m$ is not a prime number, $X$ admits a continuous selection over $[X]^m$ (subsets of $X$ of cardinality $m$). As a consequence of this, a space $X$ admits a continuous selection for every natural number if and only if the same is true for every prime number. For Hausdorff spaces $(X,τ)$ which admit continuous selections over $[X]^2$, we characterize the existence of continuous selections over $[X]^n$ for $n\geq 2$, in terms of a covering-type property.
