I am reading Martin Crossley's book, Essential Topology.

I am at present studying Example 5.55 regarding the Mobius Band as a quotient topology.

Example 5.55 Is related to Examples 5.53 and 5.54. So I now present these Examples as follows:

I cannot follow the relation

Why do we need in the relation? Indeed, why do we need ?

Surely all we need is

Can anyone explain how the relation actually works to produce the Mobius Band?

Peter