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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

10 votes
6 answers
2k views

What is an example of a topological space that is not homotopy equivalent to a CW-complex?

It would also be nice if someone can explain this comment appearing on the Wikipedia page on CW-complexes: "The homotopy category of CW complexes is, in the opinion of some experts, the best if not t …
Kevin Teh's user avatar
  • 775
31 votes
7 answers
5k views

Why is it useful to classify the vector bundles of a space?

It seems to me that vector bundles are useful because they allow us to bring to bear all of the linear algebra we know to aid in the study of topological spaces. Now, I've read somewhere that it is a …
Kevin Teh's user avatar
  • 775