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:

$H_{i}(M,M\setminus p)=0\ \forall \ i\neq n$

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.

See also point-deletion inclusion.