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text: '[summary: What do a [-3gd], a [-3rb], and a [ topological space] have in common? Each is a [-3jz] with some structure built on top of it, and in each case, we call the set the *underlying set*.]\n\n\nWhat do a [-3gd], a [-3rb], and a [ topological space] have in common? Each is a [-3jz] with some structure built on top of it, and in each case, we call the set the *underlying set*. %%note: A group is a set with an [3h7 operation], a poset is a set with an [3dt ordering], and a topological space is a set with a collection of subsets that satisfy a [ certain property].%%\n\n###Algebraic structures###\n\nAn [3gx algebraic structure] is a set equipped with operators that follow certain laws, such as a [3gd group], which is a pair $(X, \\bullet)$ where $X$ is a [3jz set] and $\\bullet$ is an operator that follows certain laws. Given an algebraic structure, we can simply throw away the operators and recover the set ($X$, in this case), which is known as the "underlying set" of the structure.\n\nThe underlying set is sometimes known as the "carrier set." Some algebraic structures have more than one underlying set; for example, a vector space is an algebraic structure built out of a [481 field] of scalars and a [3h2 commutative group], in which case the term "underlying set" is ambiguous.',
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