I'm trying to understand the suspension of a topological space: According to Wikipedia The suspension of a topological space $X$ is the quotient space $SX=(X \times I )/ \{(x_1,0) ~(x_2,0)$ and $ (x_1,1)~(x_2,1) \forall x_1,x_2 \in X \}$,$I$ is unit interval.
To understand the definition properly I'm trying some examples.Now if $X=S^n$ (n-sphere)then I can visualize that $SX$ is $ S^{n+1} $ but I'm unable in proving this rigorously.How should I prove this?