Set (Cover/Covering - Open Cover/Covering - Subcover/Subcovering)
Cover/Covering - Definition
A family 𝛾 of nonempty subsets of 𝑋 whose union contains the given set 𝑋 (and which contains no duplicated subsets) is called a cover (or covering) of 𝑋. For example:
- there is only a single cover of {1}, namely {{1}}
- there are five covers of {1,2}, namely {{1},{2}}, {{1,2}}, {{1},{1,2}}, {{2},{1,2}}, and {{1},{2},{1,2}}
The number of possible covers for a set of 𝑁 elements are:
- 1, 5, 109, 32297, 2147321017, 9223372023970362989, …
Cover/Covering - Specialized Covers
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Specialized Cover |
Description |
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is a cover for which the removal of one member destroys the covering property. For example:
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antichain covers | |
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k-covers | |
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k*-covers |