Bourbaki

Exercise 42, § 2

Topological Vector Spaces, II, p. 72

Generalise the prop. 18 of II, p. 16 to the case of an ordered set E with a Hausdorff topology for which the intervals (a,→{and}←,a)(a, \to \{ \text{and} \} \leftarrow, a) are closed for all a∈Ea \in E.

Solution

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Transcribed from the printed volume. Not translated.