Example 25.1:

Take $X = S^1$, $A = \{1\}\subset X$, $B = S^1$ and $f:A\longrightarrow B$ as $f(1) = 1$. The resulting space is the wedge of two circles $S^1\vee S^1$.

Figure: Wedge of two circles

[width=0.7]GKSBook/fig16/fig16.eps