Abstract: Let or Certain foundational questions of K-theory,
such as the existence of a stable (additive) inverse for a given
-vector bundle and the surjectivity of the natural map are investigated for spaces X
that are paracompact but not necessarily connected or finite dimensional as well
as for
-vector bundles over X that need not
have constant rank. For we show that the natural map is not surjective using elementary
techniques.More explicitly, we show
that is not in the image of the map where is the quotient map. We also show
that countable direct products of finite CW-complexes need not have the homotopy
type of a CW-complex.
Keywords and phrases: vector bundles, finite type, covering dimension.
