Geodesic
Some order properties of coverings of finite-dimensional spaces†
Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 188-197

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

Definitions and introduction. Let Ц = {Ui|i ∈ I} be a system of subsets of a normal topological space R; i.e. a mapping from the index set I into the set of all subsets of R. The order of a point x is the number of distinct member sets of Ц which contain x, and is denoted by x: Ц; the sets Ui are here considered distinct if they have distinct indices. Thus x: Ц is the number of indices i for which x ∈ Ui; ν(Ц) = max {x: Ц | x ∈ R} is called the order of the system Ц. If every point has an (open) neighbourhood meeting only finitely many members of Ц, then Ц is said to be locally finite. 
Parnaby, T. W. Some order properties of coverings of finite-dimensional spaces†. Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 188-197. doi: 10.1017/S2040618500034146
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