Article contents
On Countability of Point-Finite Families of Sets
Published online by Cambridge University Press: 20 November 2018
Extract
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).
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1979
References
- 10
- Cited by