Zeroset
This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces
Definition
A subset of a topological space is termed a zeroset if there is a continuous function from the topological space to the real numbers, such that the inverse image of zero under that continuous function is precisely that subset.
For a perfectly normal space, the zerosets are precisely the closed subsets.