We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension from a circle S to the whole space M and the cosmic expansion from a non-zero volume to the whole space-time in non-singular cosmological models. A topological analogy to the cosmic scale factor function has been suggested, the paper refers to the possible applications of the topological extension in mathematical physics.

中文翻译：

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扩展时空的新拓扑视角及其在宇宙学中的应用

我们讨论了 Tietze 扩展定理在为宇宙学中的时空扩展提供严格的拓扑基础方面的可能作用。引入了一个简单的玩具模型来显示圆的拓扑扩展之间的类比小号到整个空间米以及非奇异宇宙模型中从非零体积到整个时空的宇宙膨胀。有人提出了对宇宙尺度因子函数的拓扑类比，本文提到了拓扑扩展在数学物理中的可能应用。