论文标题
在C（x）空间之间的2-局部直径呈现图
On 2-local diameter-preserving maps between C(X)-spaces
论文作者
论文摘要
本文解决了C（x）空间之间直径的2个局部性问题。对于任何至少三个点的紧凑型Hausdorff空间X，我们在C（x）上给出了一个2局直径的映射的示例，该示例不是线性的。但是，我们表明，对于第一个可计数的紧凑型Hausdorff空间X和Y，从C（X）到C（Y）的每2个局部直径的图形都有线性，并且在某种意义上是直至常数。这产生了异构体相对于商空间的直径规范的2个代数反射性。
The 2-locality problem of diameter-preserving maps between C(X)-spaces is addressed in this paper. For any compact Hausdorff space X with at least three points, we give an example of a 2-local diameter-preserving map on C(X) which is not linear. However, we show that for first countable compact Hausdorff spaces X and Y, every 2-local diameter-preserving map from C(X) to C(Y) is linear and surjective up to constants in some sense. This yields the 2-algebraic reflexivity of isometries with respect to the diameter norms on the quotient spaces.
