How exactly does a constant identification map attach a $n$-cell? I am reading Hatcher's description of building a CW complex from $n$-skeletons. He writes that we inductively form the $n$-skeleton $X^n$ from $X^{n-1}$ by attaching $n$-cells $e_{\alpha}^n$ via maps $\phi_{\alpha}: S^{n-1} \to X^{n-1}$. Ok. So let us write the CW decomposition for $S^2$. An answer to a much earlier question states the following. ( I am writing this in the case of $S^2$ since the mental picture is easier). Let $e^0$ denote a $0$-cell and attach a $2$-cell ( a disk) to it via the constant identification map $\phi : S^{1} \rightarrow e^0.$ How does this map from the circle to the "vertice" $e_0$ attach a disk to that vertices?? I can't really picture what is happening or why this would work. And further explanation is greatly appreciated.

Imagine the 2-cell we are attaching to the point as a circular piece of paper.

Now try folding the edges of the piece of paper inwards so that the boundary collapses into a single point - sort of as if you are wrapping it around a ball, but without the ball being there.

You can't do this with real paper without it crumpling or tearing, but you can at least imagine conceptually being able to do it.

Now, when we attach a 2-cell to a point, we can visualise it as doing this "folding" to collapse the boundary to a single point and sticking it all together - and I hope it's clear that the result is indeed a 2-sphere!