Lattices of topologies of algebraic systems

The article is based on the report, which was delivered on a plenary sitting on the 5th International Algebraic Conference in the Ukraine (Odessa, July, 2005) and is a survey of the results on the lattices of topologies of different algebraic systems

Sums over Graphs and Integration over Discrete Groupoids

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as pull-back or push-forward formulas for integrals over suitable groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities fixed, and several proofs simplifie