2010/02/08 by Denis I. Saveliev, Saveliev, Denis I.
Mathematics · #08A30 #08A62 #17D19 #22A15 #22A22 #22A30 #54H25 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO #msc:08A30 #msc:08A62 #msc:17D19 #msc:22A15 #msc:22A22 #msc:22A30 #msc:54H25
paper · pdf · doi:10.48550/arxiv.1002.1599
Slides of my talk at International Conference on Analysis and Applications, January 24--26, Muscat, Oman. The results were announced at seminars on general topology in Moscow State University, 2005, and UltraMath 2008, Pisa, Italy
arxiv created 2010/02/08 · arxiv updated 2010/02/26
A classical result of topological algebra states that any compact left topological semigroup has an idempotent. We refine this by showing that any compact left topological left semiring has a common, i.e. additive and multiplicative simultaneously, idempotent. As an application, we partially answer a question related to algebraic properties of ultrafilters over natural numbers. Finally, we observe that similar arguments establish the existence of common idempotents in much more general, non-associative universal algebras.