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Let $X$ be a (real) vector space.
Let $S$ be a nonempty subset of $X$.
If $S$ is closed under addition and scalar multiplication,
then we call $S$ a subspace.
If $S$ is closed under multiplication by nonnegative scalars,
then we call $S$ a cone (that may or may not be convex).

My question is:

What do we call $S$ if $S$ is closed under scalar multiplication?

Note: $S$ need not be closed under addition.

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Following Bourbaki (EVT I.1.5 Definition 3, II.2.4 Definition 3), such a thing may be called a balanced cone.

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  • $\begingroup$ Fantastic, exactly what I was looking for. Thanks very much! $\endgroup$
    – max_zorn
    Feb 2 '19 at 20:15

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