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Results tagged with gn.general-topology
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user 2625
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
0
votes
1
answer
386
views
The functor of continuous functions from compact CW-spaces to the reals
The contravariant functor $C(-)$ given by
$$
\hom_{Top}(-,\mathbb{R}):cCW\to Rng
$$
where $cCW$ is the category of compact CW complexes is injective on objects. What is known about surjectivity, faith …
- 2,782
39
votes
3
answers
6k
views
Why do finite homotopy groups imply finite homology groups?
Why does a space with finite homotopy groups [for every n] have finite homology groups? How can I proof this [not only for connected spaces with trivial fundamental group]? The converse is false. $\ma …
- 2,782
7
votes
2
answers
412
views
Relation between $KO$ and $K$
What can be said about the relation between the complex and the real K-theory of a CW complex? An $n$-dimensional complex vector bundle is an $2n$-dimensional real vector bundle but not vice versa. Yo …