Free regular set

In mathematics, a free regular set is a subset of a topological space that is acted upon disjointly under a given group action.

To be more precise, let X be a topological space. Let G be a group of homeomorphisms from X to X. Then we say that the action of the group G at a point ${\displaystyle x\in X}$ is freely discontinuous if there exists a neighborhood U of x such that ${\displaystyle g(U)\cap U=\varnothing }$ for all ${\displaystyle g\in G}$, excluding the identity. Such a U is sometimes called a nice neighborhood of x.

...
Wikipedia