The partition does not contain the four corners of the unit square, is this a legit partition since the union of elements in the partition is unit square without the four corners? If u see this pls upvote it so more people can see this post, this really confused me.
In introduction to topology by colin adams, example 3.19, he constructed a Möbius band from a unit square by defining a partition with elements A_(x,y)={(x,y)} for 0<x<1 and 0<=y<=1, and B*_y={(0,y), (1,1-y)} with 0<y<1. Why are the four corners on the square not included in glueing? Isn't the union of elements in a partition of X always X? Now the union of these elements is a square without the four corners... Can anyone answer it for me? I really got confused .