Suspension pushes up connectivity by one

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Statement

Define, for a topological space X, the connectivity of X as follows:

The connectivity of the Suspension (?) SX is exactly one more than the connectivity of X.

In particular, X is a weakly contractible space if and only if SX is.

Facts used

  1. Suspension of any space is path-connected
  2. Suspension of path-connected space is simply connected
  3. Homology for suspension
  4. Hurewicz theorem

Proof

The proof essentially follows from facts (1)-(4).