紧集理论的计算机验证
A Computer Verified Theory of Compact Sets
摘要：
构造性数学中的紧集捕捉了我们对平面（或任何其他完备度量空间）的可计算子集应该是什么的直觉。紧集的良好表示提供了用计算机创建和显示图像的有效手段。在本文中，我建立在现有的工作，完全度量空间，定义为有限集的空间在Hausdorff度量下的完备紧集。这个定义使我能够迅速开发出一个计算机验证的紧集理论。我应用这个理论来计算一致连续函数的可证明正确的图。
英文摘要：
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and displaying images with a computer. In this paper, I build upon existing work about complete metric spaces to define compact sets as the completion of the space of finite sets under the Hausdorff metric. This definition allowed me to quickly develop a computer verified theory of compact sets. I applied this theory to compute provably correct plots of uniformly continuous functions.
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