I am studying algebraic topology and I am a beginner in it. I want to prove that if $ (X, x_0) \sim (Y, y_0) $ and $(Z, z_0) \sim (W , w_0) $ then $ X\vee Z \sim Y\vee W .$ X,Y, Z, W are top spaces
I have just an intuition that wedge product seems something like glueing two spaces together in a point. I don't know how can I start to think about it and solve it. Any help would be great thanks.