A Lie subalgebra (subspace that is closed under the Lie bracket) ๐ of a given Lie algebra ๐ such that the Lie bracket [๐,๐] is a subset of ๐.
A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.
A subring closed under multiplication by its containing ring.
A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.
A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
Not actually present, but considered as present when limits at infinity are included.
Optimal; being the best possibility.
Existing only in the mind; conceptual, imaginary.
Pertaining to ideas, or to a given idea.
Perfect, flawless, having no defects.
Teaching or relating to the doctrine of idealism.
given two vectors v,w, |v+w|<|v|+|w| (the triangle inequality).
if v ne 0 then |v| ne 0;
That which is normal or typical.
A high level of performance in a chess tournament, several of which are required for a player to receive a title.
A rule that is imposed by regulations and/or socially enforced by members of a community.
A sentence with non-descriptive meaning, such as a command, permission, or prohibition.
given a scalar k, |kv|=|k|ยท|v|, where |k| is the absolute value of k;
To endow (a vector space, etc.) with a norm.