Geodesic
On Countability of Point-Finite Families of Sets
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 673-679

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

It is well known that in a separable topological space every point-finite family of open subsets is countable. In the following we are going to show that both in σ-finite measure-spaces and in topological spaces satisfying the countable chain condition, point-finite families consisting of “large” subsets are countable. Notation and terminology. Let A be a set. The family consisting of all (finite) subsets of A is denoted by . Let be a family of subsets of A. The sets and are denoted by and , respectively. We say that the family is point-finite (disjoint) if for each a ∈ A , the family has at most finitely many members (at most one member). 
Junnila, Heikki J. K. On Countability of Point-Finite Families of Sets. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 673-679. doi: 10.4153/CJM-1979-067-8
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