Homologically Euclidean point

Definition
A point $$p$$ in a topological space $$M$$ is termed homologically $$n$$-Euclidean if:

$$H_n(M, M \setminus p) = \mathbb{Z}$$

and:

$$H_i(M, M \setminus p) = 0 \ \forall \ i \ne n$$

Stronger properties

 * Hausdorff-Euclidean point
 * Closed Euclidean point

In particular any point in a $$n$$-manifold or a $$n$$-locally Euclidean space is homologically $$n$$-Euclidean.

See also point-deletion inclusion.