February 2, 1998. A.A.Ivanov. Topologies on products and function spaces

There are a surprising connections between topological structures on products XxY and topological structures on spaces of functions (mappings) Y/Z - in other definitions C(Y,Z), Z^Y. Not going into details we say that for a topological structure T on X/Y there exists the corresponding (conjugate) topological structure T^* on Y/Z and for a topological structure T on Y/Z there exists the corresponding (conjugate) topological structure T_* on XxY. If (T_*)^*=T ((T^*)_*=T), then the topological structures T and T_* (T and T^*) are called dual ones. For example, the usual topology on XxY and the compact- open topology on Y/Z are dual, the topology of pointwise convergence on Y/Z and the topology on XxY defined by convergencies of directed systems of points stationary for some co-ordinate are dual too.

List of talks at previous sessions of the seminar.