Cardinal invariants: various aspects of the theory
by
A.V. Arhangel'skii
Ohio University, Athens, Ohio, 45701

Cardinal invariants play, or can play, an important role in every domain of general topology. Enough to say that many convergence phenomena are clearly expressed in terms of cardinal invariants. Thus, the more general and elementary part of the theory of cardinal invariants is one of those elephants on which general topology stands. However, deeper, or more fundamental, results in each of these domains have their own flavour, their own colour, reflecting the specifics of it. The problems arising also require special techniques depending on the domain.

In the talk, we will discuss several recent results on cardinal invariants and open problems, demonstrating versatility of the subject.

The topics we will touch upon include the following: cardinal invariants and the diagonal properties, cardinal invariants and submetrizability, cardinal invariants and topological and paratopological groups, cardinal invariants and remainders in Hausdorff compactifications, cardinal invariants and the topology of function spaces.

The talk is not a survey, just a sample of results will be presented.

Date received: March 1, 2006