Is there a name for a collection of sets with the following property?
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Is there a conventional name (term) for a collection $mathbb{S}$ of sets with the following property: for any natural $k$ and $A_1,...,A_kin mathbb{S}$ there are $m,ngeq 0$ and pairwise disjoint $B_1,...,B_{m+n}in mathbb{S}$ such that $bigcuplimits_{i=1}^m B_i = bigcuplimits_{i=1}^k A_i$ and $bigcuplimits_{i=1}^{m+n} B_i in mathbb{S}$?
elementary-set-theory terminology
asked Jan 12 at 9:47
MikhailMikhail
605
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add a comment |
$begingroup$
Is there a conventional name (term) for a collection $mathbb{S}$ of sets with the following property: for any natural $k$ and $A_1,...,A_kin mathbb{S}$ there are $m,ngeq 0$ and pairwise disjoint $B_1,...,B_{m+n}in mathbb{S}$ such that $bigcuplimits_{i=1}^m B_i = bigcuplimits_{i=1}^k A_i$ and $bigcuplimits_{i=1}^{m+n} B_i in mathbb{S}$?
elementary-set-theory terminology
asked Jan 12 at 9:47
MikhailMikhail
605
$endgroup$
add a comment |
$begingroup$
Is there a conventional name (term) for a collection $mathbb{S}$ of sets with the following property: for any natural $k$ and $A_1,...,A_kin mathbb{S}$ there are $m,ngeq 0$ and pairwise disjoint $B_1,...,B_{m+n}in mathbb{S}$ such that $bigcuplimits_{i=1}^m B_i = bigcuplimits_{i=1}^k A_i$ and $bigcuplimits_{i=1}^{m+n} B_i in mathbb{S}$?
elementary-set-theory terminology
asked Jan 12 at 9:47
MikhailMikhail
605
$endgroup$
Is there a conventional name (term) for a collection $mathbb{S}$ of sets with the following property: for any natural $k$ and $A_1,...,A_kin mathbb{S}$ there are $m,ngeq 0$ and pairwise disjoint $B_1,...,B_{m+n}in mathbb{S}$ such that $bigcuplimits_{i=1}^m B_i = bigcuplimits_{i=1}^k A_i$ and $bigcuplimits_{i=1}^{m+n} B_i in mathbb{S}$?
elementary-set-theory terminology
elementary-set-theory terminology
asked Jan 12 at 9:47
MikhailMikhail
605
asked Jan 12 at 9:47
MikhailMikhail
605
asked Jan 12 at 9:47
MikhailMikhail
605
asked Jan 12 at 9:47
MikhailMikhail
605
asked Jan 12 at 9:47
MikhailMikhail
605
605
add a comment |
add a comment |
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