Suspension of path-connected space is simply connected

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Statement

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

Related facts

Applications

Facts used

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

Proof

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