We give an exposition of Novodvorskii’s theorem in Banach algebra K-theory, asserting that the Gelfand transform for a commutative induces isomorphism topological K-theory.

There is a natural way to define an isomorphism between the group of transformations of isotopy classes of rational tangles and the modular group. This isomorphism allows to give a simple proof of the Conway theorem, stating the one-to-one correspondence between isotopy classes of rational tangles and rational numbers. Two other simple ways to define this isomorphism, one of which suggested by ...

We prove an equivariant analogue of Chevalley’s isomorphism theorem for polynomial, C∞ or Cω maps.

For a large class of separable Banach spaces, we prove the real analytic Dolbeault isomorphism theorem for open subsets.

A classical theorem of Steinitz [I& p. 1251 states that the characteristic of an algebraically closed field, together with it.s absolute degree of transcendency, uniquely det,ermine the field (up to isomorphism). It is easily seen that the word real-closed cannot be substituted for the words algebraically closed in this theorem. It is therefore natural to inquire what invariants other than the ...

One can associate a polymatroid with a hypergraph that naturally generalises the cycle matroid of a graph. Whitney's 2-isomorphism theorem characterises when two graphs have isomorphic cycle matroids. In this paper Whitney's theorem is generalised to hypergraphs and polymatroids by characterising when two hyper-graphs have isomorphic associated polymatroids. 1997 Academic Press

There does not exist an isomorphism-invariant Borel version of the Higman-Neumann-Neumann Embedding Theorem.