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Iosif Pinelis
Iosif Pinelis
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Let E$E$ be a set, and let S$S$ be any set of subsets of E$E$, such that S$S$ contains the emptysetempty set. Can you identify the smallest set of subsets T$T$ of E$E$ such that T$T$ contains all elements of S$S$, and T$T$ is stable by both finite union and by any intersections ? If possible write the generic form of an élémentelement of T$T$ by using élémentselements of S$S$, with unions and intersections.

Let E be a set, and let S be any set of subsets of E, such that S contains the emptyset. Can you identify the smallest set of subsets T of E such that T contains all elements of S, and T is stable by both finite union and by any intersections ? If possible write the generic form of an élément of T by using éléments of S, with unions and intersections.

Let $E$ be a set, and let $S$ be any set of subsets of $E$, such that $S$ contains the empty set. Can you identify the smallest set of subsets $T$ of $E$ such that $T$ contains all elements of $S$, and $T$ is stable by both finite union and by any intersections ? If possible write the generic form of an element of $T$ by using elements of $S$, with unions and intersections.

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Guest2024bis
Guest2024bis
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Smallest ensemble of sets stable by any intersections and finite union

Let E be a set, and let S be any set of subsets of E, such that S contains the emptyset. Can you identify the smallest set of subsets T of E such that T contains all elements of S, and T is stable by both finite union and by any intersections ? If possible write the generic form of an élément of T by using éléments of S, with unions and intersections.