In this figure I circled half of the inner radius of a Mobius band that I used to construct a holed cross cap. I don't know if it is required to exist to do the self intersection because I read somewhere on this site that aside from the zip-pair construction the holed cross cap is also the limit as the inner radius used for the Mobius band approaches $0$.
My question is if that is true then does the limit of that Mobius band as the inner radius approaches $0$ still has an inner radius?
