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

论度量空间的可计算性结构、维数和描述集合论的复杂性

• 批准号: 19540086
• 负责人: HATTORI Yasunao
• 金额: $ 2.08万
• 依托单位: Shimane University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540086/
• 关键词: トポロジー; 情報基礎; 距離空間; ドメイン; 次元; 超限次元; ボレルクラス; 双曲型位相; 形式的球体; ノルム空間; 超空間位相; ボレル集合; 位相次元; 計算可能性

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

本文从拓扑的角度研究了度量空间的可计算性。我们还研究了拓扑空间的集合论拓扑和维数理论。特别地，我们研究了度量空间的形式球的域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）和模绝对加法类A（α）的归纳维数，并构造了这些维数值不同的例子.我们还改进了归纳维数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，并利用多值映射的选择给出了强仿紧性的一个刻划

项目成果

Order and topological structures of posets of the formal balls on metric spaces

度量空间上形式球偏序集的序和拓扑结构

• 发表时间: 2010
• 期刊: Memoirs Faculty Sci. Engi. Shimane Univ. Ser. B Vol.43
• 作者: T. Sasak;M. Yoshida;Yasunao Hattori
• 通讯作者: Yasunao Hattori

Transfinite large inductive dimensions modulo absolute Borel classes

超限大感应维数模绝对 Borel 类

• 发表时间: 2009
• 期刊: J. Math. Soc. Japan Vol.61
• 作者: Vitalij Chatyrko;Yasunao Hattori
• 通讯作者: Yasunao Hattori

The chain recurrent set for maps of compacta

Compacta 映射的链循环集

• 发表时间: 2007
• 期刊: Annales Polonici Mathematici 92
• 作者: K. Kiyohara;P. Topalov;T.Morimoto;Tohru Morimoto;T. Morimoto;Tohru Morimoto;T. Morimoto;Tohru Morimoto;M. Kimura;Katsuya Yokoi
• 通讯作者: Katsuya Yokoi

Strong paracompactness and multi-selections

强拟紧性和多重选择

• 期刊: Topology and its Applications
• 影响因子: 0.6
• 作者: Valentin Gutev;Takamitsu Yamauchi
• 通讯作者: Takamitsu Yamauchi

Addition and product theorems for ind

ind 的加法和乘积定理

• 发表时间: 2008
• 期刊: Topology and its Applications 155
• 作者: V. Chatyrko;Y. Hattori
• 通讯作者: Y. Hattori