Convergence-theoretic unification in general topology
by
Szymon Dolecki
Burgundy Institute of Mathematics

In the last ten years various concepts and theorems of general topology have been studied from the point of view of functorial inequalities in convergence theory. The study mainly concerned properties defined through few simple constructions with the aid of several special classes of filters.

The range of applications turned out to be unexpectedly rich. It includes interactions between various types of quotient, perfect and covering maps with numerous classes of properties of spaces.

Important aspects of the approach are unity and simplicity. The unity consists in the existence of few general theorems, abundant special cases of each of which coincide with classical theorems. The simplicity is due to two calculi developed along the study. Calculus of functorial inequalities enables one to considerably reduce many arguments based on diagrams. Calculus of families of relations and sets offers a versatile treatment of interactions in product spaces.

Date received: June 16, 2006