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level set (Definition)

Let $ A$ and $ B$ be sets and $ f$ a function mapping $ A$ into $ B$. Then the sets

$\displaystyle \{ x \mid f(x) = y \}$
where $ y \in B$ are known as the level sets (or fibres) of $ f$.



"level set" is owned by yark. [ full author list (2) | owner history (1) ]
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See Also: fibre, level curve


Attachments:
level sets of smooth functions on manifolds (Definition) by rspuzio
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Cross-references: mapping, function
There are 4 references to this entry.

This is version 3 of level set, born on 2004-12-13, modified 2005-07-22.
Object id is 6569, canonical name is LevelSet.
Accessed 2481 times total.

Classification:
AMS MSC: 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )
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