Relations between the real projective space and canonical covering projections
Let be the canonical covering projection. For any map define the space
and the covering projection
i) What is the fibre of ?
ii) For any space establish a one-one correspondence between maps and pairs of maps such that .
iii) Let , the space with two points . For define a homeomorphism x such that
I think i) is relatively straightforward and I get for a given there are two points with such that . So .
However I'm struggling with the next two, any help appreciated...