Collapse map of degree one onto a sphere
= Collapse map of degree one onto a sphere
{title2=$M^n\longrightarrow M/(M\setminus\operatorname{int}D^n)\cong S^n$}
Choose an oriented embedded closed disc in a closed oriented positive-dimensional manifold and collapse its complement to a point. A target point away from the collapsed value has one preimage with local degree $+1$, proving global degree one by the <degree as a sum of local degrees>.