Hausdorff-Euclidean point

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.

Weaker properties

 * Euclidean point
 * Nondegenerate point
 * Closed Euclidean point
 * Homologically Euclidean point