On the structure of computability on metric spaces, dimension and the complexities of descriptive set theory

从拓扑学的角度研究了度量空间的可计算性。我们还研究了集论拓扑学和拓扑空间的维度理论。特别地，我们研究了度量空间的形式球的整环上的序与拓扑结构之间的关系。在维数理论方面，我们研究了模绝对乘法类M(α)和加法类A(α)的诱导维数，并构造了它们的数值差异的例子。我们还改进了关于归纳维度的加法定理和乘积定理。我们还考虑了局部紧子空间的有限并空间，并通过多值映射的选择给出了强仿紧性的一个刻画

We studied about the computability of metric spaces from the topological point of view. We also studied on set-theoretic topology and dimension theory of topological spaces. In particular, we studied the relations between the order and topological structures on the domains of the formal balls of metric spaces. Concerning dimension theory, we investigated the inductive dimension modulo absolute multiplicative class M(α) and additive class A(α), and constructed the examples which show the differences of the values of these dimensions. We also improved the additive theorem and the product theorem for the inductive dimensions. We also considered the spaces which are finite union of locally compact subspaces and gave a characterization of strong paracompactness by means of the selection of multi-valued mappings