There are things I don't understant in your explanation. F, as defined, seems to be en element of Q/~ X Q/~ while C1,C2 and C3 are in Q X Q
Hi, everyone,
I resolved the following exercise. I need help reviewing it and giving the correct answer (if mine isn't correct of course).
Let's have:
where the following equivalence relation is defined
, if or ,
Prove that is closed.
Solution:
is connected and compact so even must be connected and compacted. At this point we have to prove that is (Hausdorff). That is to prove that the set
is closed on .
,
.
is closed because is . , are closed being subspaces of space and immages of the compact on through continuous applications. Because then even will be closed, this means that is . I conclude that is closed.