On Countability of Point-Finite Families of Sets
1979 ◽
Vol 31
(4)
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pp. 673-679
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Keyword(s):
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).
1976 ◽
Vol 19
(3)
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pp. 337-341
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Keyword(s):
1993 ◽
Vol 704
(1 Papers on Gen)
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pp. 269-272
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1975 ◽
Vol 13
(2)
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pp. 241-254
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Keyword(s):
1991 ◽
Vol 112
(4)
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pp. 1125
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Keyword(s):
1998 ◽
Vol 188
(1-3)
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pp. 205-223
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1974 ◽
Vol 4
(4)
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pp. 315-339
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Keyword(s):
1982 ◽
Vol 25
(3)
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pp. 425-431
Keyword(s):