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:

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

Relation with other properties

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.