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.
A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.
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.
A value to which a sequence converges. Equivalently, the common value of the upper limit and the lower limit of a sequence: if the upper and lower limits are different, then the sequence has no limit (i.e., does not converge).
A restriction; a bound beyond which one may not go.
The cone of a diagram through which any other cone of that same diagram can factor uniquely.
A determining feature; a distinguishing characteristic.
Fixed limit.
The final, utmost, or furthest point; the border or edge.
The first group of riders to depart in a handicap race.
A person who is exasperating, intolerable, astounding, etc.
Any of several abstractions of this concept of limit.
To restrict; not to allow to go beyond a certain bound, to set boundaries.
To have a limit in a particular set.
Being a fixed limit game.