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Reconstructing the topology of clones

Authors: Manuel Bodirsky, Michael Pinsker and András Pongrácz
Journal: Trans. Amer. Math. Soc. 369 (2017), 3707-3740
MSC (2010): Primary 03C05, 03C40, 08A35, 20B27; Secondary 08A70
Published electronically: January 6, 2017
MathSciNet review: 3605985
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Abstract: Function clones are sets of functions on a fixed domain that are closed under composition and contain the projections. They carry a natural algebraic structure, provided by the laws of composition which hold in them, as well as a natural topological structure, provided by the topology of pointwise convergence, under which composition of functions becomes continuous. Inspired by recent results indicating the importance of the topological ego of function clones even for originally algebraic problems, we study questions of the following type: In which situations does the algebraic structure of a function clone determine its topological structure? We pay particular attention to function clones which contain an oligomorphic permutation group, and discuss applications of this situation in model theory and theoretical computer science.

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Additional Information

Manuel Bodirsky
Affiliation: Institut für Algebra, TU Dresden, 01062 Dresden, Germany

Michael Pinsker
Affiliation: Department of Algebra, MFF UK, Sokolovska 83, 186 00 Praha 8, Czech Republic

András Pongrácz
Affiliation: Department of Algebra and Number Theory, University of Debrecen, 4032 Debrecen, Egyetem Square 1, Hungary

Received by editor(s): January 23, 2014
Received by editor(s) in revised form: February 29, 2016
Published electronically: January 6, 2017
Additional Notes: The first and third authors have received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 257039). The first author also received funding from the German Science Foundation (DFG, project number 622397)
The second author has been funded through projects I836-N23 and P27600 of the Austrian Science Fund (FWF). The third author was also partially supported by the Hungarian Scientific Research Fund (OTKA) grant no. K109185.
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