Geodesic
Extended Schauder decompositions of locally convex spaces†
Glasgow mathematical journal, Tome 15 (1974) no. 2, pp. 166-171

Voir la notice de l'article provenant de la source Cambridge University Press

Let E[τ] be a locally convex Hausdorff topological vector space. An extended decomposition of E[τ] is a family {Ea}α∈A of closed subspaces of E such that, for each x in E and each α in A, there exists a unique point xα in Eα, with Here convergence will have the following meaning. Let Ф denote the set of all finite subsets of A. The sum is said to be convergent to x if for each neighbourhood U of 0 in E, there is an element φ0 of Ф such that , for all φ in Ф containing φ0. It follows that is Cauchy if and only if, for each neighbourhood U of 0 in E, there is an element φ0 of Ф such that , for all φ in Ф disjoint from φ0. 
Webb, J. H. Extended Schauder decompositions of locally convex spaces†. Glasgow mathematical journal, Tome 15 (1974) no. 2, pp. 166-171. doi: 10.1017/S0017089500002366
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