How is the following a CW complex

Question

My professor today draw on the board a sphere and attached to half a circle of the sphere half of the boundary of a disk so the shape looked like you glue a curvy half disk to a sphere. He then said that this is obviously a CW complex but I don't see how. I know that we can certainly construct our shape by first attaching the boundary of a 2 cell to a zero cell to obtain a sphere and then attaching the half of the boundary of another 2 cell to half a circle of the sphere. The problem is that the definition of the CW complex only allows me to attach 2 cells in the one skeleton as such my second attachment is not allowed. Can anyone please tell me if I am saying anything wrong here and what is the CW complex structure of our shape?
Thanks in advance

Answer 1

you can begin whit two point,then attach three one_cell to obtain two circle whit a common semicircle.then attach two 2_cell from both sides to a circle to obtain the sphere and one 2_cell to another circle to obtain the disk.

Answer 2

it is a CW-complex...

starting with two point ...attach two one cell to construct a circle figure...then attach a two cell with a 1 cell to define a figure like sphere with a loop connecting north and south pole...then you add another 2-cell attaching each half-circle of the boundary of the 2-cell with an edge of 1-skeleton....and finally you'll get the picture

Answer 3

I'm in favour of some pictures of cell complexes, so here are two, taken from the book Topology and Groupoids:

Of course the first is of dimension $1$ and the second is of dimension $2$.