Given a topological groupG (usually compact abelian), the authors study the poset D = D(G) of dense subgroups of G and its impact on the algebraic structure of G. A key tool for this is the subgroup den(G) := ∩ D. Definition. For a cardinal κ ≥ 1, a topological group is in the class Ff (κ) [F(κ); F2(κ); Fad(κ), respectively] if some family of κ-many dense subgroups of G is independent and freel...

Here a typical topological semigroup C(G) is studied. A partial equivalence [1] is defined on C(G) compatible with its semigroup structure. Also a uniformity is constructed giving the Vietoris topology [3] on C(G).

In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. In particular, we introduce some generalization of the Brauer group in the topological context and show that any its element can be represented as a locally trivial bundle with the structure group N × k , k ∈ N . Finally, we discuss its possible applications in the twiste...

We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H(BG,Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involve...