Geodesic
On Σ-Finite Families
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 481-488

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

Let be a family of subsets of a topological space X. We do not require to be a covering of X, nor do we assume that the members of are necessarily open. In this paper we shall assume that is of a special sort, which we call Σ-Finite. We show that a Σ-Finite family is both locally finite and star-finite, and in particular that an open covering of X is Σ-Finite if and only if it is star-finite. We then prove that every Σ-Finite family is ᓂ-discrete, so that in particular, every star-finite open covering of X is (ᓂ-discrete. There seems to be some applications of this fact. 
Mccandless, Byron H. On Σ-Finite Families. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 481-488. doi: 10.4153/CJM-1975-057-x
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