关于用g函数刻画的一些空间

ON SOME SPACES CHARACTERIZED IN TERMS OF g-FUNCTIONS

本文研究了强α空间在有限到一的闭映射下的映射性质问题.利用闭映射的等价刻画构造g函数,获得了强α空间在有限到一的闭映射下保持的结果,改进了强α空间在有限到一的既开又闭映射下保持的结果.本文还研究了σ空间的半层对应刻画.

In this note, we study the property of strongly a-spaces under finite-to-one closed maps. By using equivalent characterizations of closed maps to construct g-functions, we prove that strongly α-spaces are preserved under finite-to-one closed maps, this result improves that strongly α-spaces are preserved under finite-to-one open and closed maps. we also characterize σ-spaces in terms of semistratifiable operator.