In this work, we consider a decreasing sequence of groups \(\left( G_{n}\right) _{n\ge 1}\) provided with the structures of Banach manifolds and satisfying some conditions, then we show that the group \(G_{\infty }=\bigcap _{n\ge 1}G_{n}\) equipped with the projective topology is a regular Lie–Fréchet group. We use this result to prove the regularity of some Fréchet–Lie groups.

中文翻译：

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关于一类正规的弗雷谢特-李群

在这项工作中，我们考虑具有Banach流形结构且满足某些条件的\（\ left（G_ {n} \ right）_ {n \ ge 1} \）组的递减序列，然后证明该组配有射影拓扑的\（G _ {\ infty} = \ bigcap _ {n \ ge 1} G_ {n} \）是一个常规的L​​ie–Fréchet组。我们用这个结果来证明某些弗雷谢特-李群的规律性。