2
votes
1answer
45 views

Is there a topological space and meanwhile a linear space such that its vector addition is discontinuous but scalar multiplication is continuous?

The title is the question. Does there exist a topological space and meanwhile a linear space X such that its vector addition operation is discontinuous but scalar multiplication operation is ...
2
votes
0answers
175 views

Hairy ball theorem: references to applications

I'm looking for references to applications of the Hairy ball theorem. I already visited wikipedia and cited references, but I need a little more explanation in both meteorology and applications in ...
1
vote
1answer
188 views

Understanding Hom-bundle on vector bundles (Atiyah)

I am trying to make sense of the following statment (from Atiyah's K-theory book) Suppose $V,W$ are vector spaces, and that $E=X \times V, F=X \times W$ are the corresponding product bundles. Then ...
2
votes
1answer
136 views

Simple Continuity Question concerning Vector Bundles

I'm a bit confused about the following part in Sir Michael Atiyah's "K-Theory." Let $E = X \times V$ and $F = X\times W$, and let $\phi: E\to F$ be a vector bundle homomorphism. Why is the induced ...