Long Line和其它非仿紧流形在局部凸空间中的光滑嵌入
Smooth embeddings of the Long Line and other non-paracompact manifolds into locally convex spaces
摘要：
我们证明了每一个有限维Hausdorff（不一定是仿紧的，不一定是第二可数的）$C^r$ -流形可以嵌入到一个弱完备向量空间中，即一个局部凸拓扑向量空间的形式为${\mathbb R}^I$的不可数指标集$I$，并确定了这种嵌入是可能的$I$的最小基数.
英文摘要：
We show that every finite dimensional Hausdorff (not necessarily paracompact, not necessarily second countable) $C^r$-manifold can be embedded into a weakly complete vector space, i.e. a locally convex topological vector space of the form ${\mathbb R}^I$ for an uncountable index set $I$ and determine the minimal cardinality of $I$ for which such an embedding is possible.
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。
