The identity map
(1)
is a continuous bijection by . Its domain is compact by part (i), and its codomain is a Hausdorff space because every metric space is Hausdorff. The compact-to-Hausdorff continuous bijection theorem therefore makes the identity a homeomorphism. Consequently
(2)

Ancestors (10)

  1. 10E
  2. Paper 2
  3. ib
  4. 2020
  5. Past exam of the mathematics course of the University of Cambridge
  6. Mathematics course of the University of Cambridge
  7. Course of the University of Cambridge
  8. University of Cambridge
  9. List of universities
  10. Home

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version