# Suspension of path-connected space is simply connected

From Topospaces

## Statement

Suppose is a Path-connected space (?). Denote by the Suspension (?) of . Then, is a Simply connected space (?).

## Related facts

### Applications

- n-sphere is simply connected for n greater than 1: The -sphere is the suspension of the -sphere .

## Facts used

- Union of two simply connected open subsets with path-connected intersection is simply connected, which in turn uses the Seifert-van Kampen theorem

## Proof

*Fill this in later*