Hausdorff-Euclidean point
This article defines a property that one can talk about for a pair of a topological space and a point in it
Definition
A point in a topological space is termed Hausdorff-Euclidean if the point has an open neighbourhood homeomorphic to Euclidean space such that every point inside the open neighbourhood can be separated from any point outside the open neighbourhood by disjoint open sets.
Note that for a Hausdorff space, any Euclidean point is Hausdorff-Euclidean.