Topological Algebra

Staff: Dr Yann Peresse

Topological Algebra studies the interplay of Topology and Algebra. Specifically, it concerns algebraic objects which have a topology that makes their operations continuous. The real numbers form a familiar example, having both an algebraic structure (we can add and multiply them) and a topological structure (they have converging sequences and continuous functions). Crucially, these two structures interact nicely: if x is roughly 3 and y is roughly 5, then x+y is roughly 8 and xy roughly 15.

Some topics that we are particularly interested in:

  • Topological groups, semigroups and inverse semigroups.
  • The product topology on transformation semigroups.