- #1
Bacle
- 662
- 1
Hi, All:
I was thinking of the result that every compact metric space is the continuous image
of the Cantor set/space C. This result is built on some results like the fact that 2nd
countable metric spaces can be embedded in I^n (I is --I am?-- the unit interval),
the fact that there is a continuous map between C and I, and, from what I read
recently , the fact that every closed subset of C is a retract of C.
How do we know that every closed subset of C is a retract of C?
I was thinking of the result that every compact metric space is the continuous image
of the Cantor set/space C. This result is built on some results like the fact that 2nd
countable metric spaces can be embedded in I^n (I is --I am?-- the unit interval),
the fact that there is a continuous map between C and I, and, from what I read
recently , the fact that every closed subset of C is a retract of C.
How do we know that every closed subset of C is a retract of C?