MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In Spanier's Algebraic Topology, he defined CW complexes assumed an additional strange condition: the cell must have the coherent topology with the characteristic map and the inclusion map of its boundary. What is the meaning of this condition? Some other author seems never use it, and they asked the space to be Hausdorff. Are the CW complexes Hausdorff in Spanier's way? Do the various definitions agree? Thanks!

share|cite|improve this question
3 would be a good website for your question. I think it would be a good idea to put a little more effort into it and list the definitions you're referring to. People likely do not have the textbooks you're referring to on hand. – Ryan Budney Mar 21 '12 at 9:27
I thought this had been answered in… – Ronnie Brown Mar 25 '12 at 10:04

It basically says that a CW complex has the coherent topology from its closed cells. This should be wrapped up into any definition of a CW complex that you see.

For example in Massey's book it is equivalent to statement (iv):

A subset $A$ is closed if and only if $A \cap \bar{e}$ is closed for all $n$-cells, $e^n,n=0,1,2,\ldots$

(You can see this equivalence at the wikipedia page).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.