合成拓扑与构造性度量空间
Synthetic Topology and Constructive Metric Spaces
摘要：
本论文主要研究综合拓扑，特别是与度量空间的关系。综合拓扑模型是一个范畴模型，其中对象在适当的意义上具有一个内在拓扑，并且所有态射关于它是连续的.我们重新定义了综合拓扑，以便包含闭集，并作了几个推广.实数被重构（以适应新的背景）为开放的戴德金割。一个广泛的理论时，度量和内在拓扑匹配。最后，在四个具体的模型中检查结果。
英文摘要：
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are continuous with regard to it. We redefine synthetic topology in order to incorporate closed sets, and several generalizations are made. Real numbers are reconstructed (to suit the new background) as open Dedekind cuts. An extensive theory is developed when metric and intrinsic topology match. In the end the results are examined in four specific models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
