Definitions
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adjective
Coming from or found in the area near you.
Examples
- We prefer to buy local vegetables.
- The local bakery opens at six every morning.
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adjective
Stored on your own computer, not on a network or server.
Examples
- I saved a local copy of the file.
- The program keeps a local disk cache for speed.
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adjective
In programming, only usable inside one part of a program.
Examples
- Declare the variable as local so it stays inside the function.
- Local variables disappear once the function returns.
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adjective
Affecting only one small part of the body.
Examples
- The doctor used local anesthesia on my hand.
- The rash was local and did not spread.
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adjective
In mathematics, true in a small area around every point.
Examples
- This space has a local property at every point.
- The shape looks flat when you check it locally.
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adjective
In mathematics, true for arbitrarily small areas around every point.
Examples
- The space is local because every point has tiny neighborhoods with the property.
- Mathematicians study local compactness in this space.
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adjective
In group theory, true when every small part of the group has the property.
Examples
- A group is local if each finitely generated part has the property.
- We checked the local property one subgroup at a time.
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adjective
In algebra, true for an object when it is true in each of its simpler local versions.
Examples
- Flatness is a local property in algebra.
- Being finitely generated is not a local property.
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adjective
In group theory, showing up in the behavior of certain smaller parts of a group.
Examples
- The theorem shows this property is local.
- Group theorists call such a property local for this reason.
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adjective
In algebra, having exactly one largest ideal.
Examples
- A local ring has exactly one maximal ideal.
- The theorem applies only to local rings.