Pettis property for Polish inverse semigroups




Inverse topological semigroups, Polish semigroups, Pettis theorem, automatic continuity


We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity.


Download data is not yet available.

Author Biographies

Karen Arana, Industrial University of Santander

Escuela de Matemáticas

Jerson Pérez, Industrial University of Santander

Escuela de Matemáticas

Carlos Uzcátegui, Industrial University of Santander

Escuela de Matemáticas


J. Carruth, H. Hildebrant, and R. Koch, The theory of topological semigroups, Monographs and Textbooks in Pure and Applied Mathematics vol. 75, Marcel Dekker, Inc., New York, 1983.

L. Elliott, J. Jonušas, Z. Mesyan, J. D. Mitchell, M. Morayne, and Y. P'eresse, Automatic continuity, unique Polish topologies, and Zariski topologies (Part I, monoids),, 2020.

L. Elliott, J. Jonušas, J. D. Mitchell, Y. Péresse, and M. Pinsker, Polish topologies on endomorphism monoids of relational structures,, 2022.

O. V. Gutik, J. Lawson, and D. Repovš, Semigroup closures of finite rank symmetric inverse semigroups, Semigroup Forum 78, no. 2 (2009), 326-336.

O. V. Gutik, and A. R. Reiter, Symmetric inverse topological semigroups of finite rank ≤ n, Mat. Metodi Fiz.-Mekh. Polya 52, no. 3 (2009), 7-14.

J. Howie, Fundamentals of semigroup theory, London Mathematical Society Monographs. New Series 12. Oxford University Press, New York, Second Edition, 2003.

A. Kechris, Classical Descriptive Set Theory. Graduate Texts in Mathematics 156. Springer-Verlag, New York, 1995.

A. Kechris, and C. Rosendal, Turbulence, amalgamation, and generic automorphisms of homogeneous structures, Proc. Lond. Math. Soc. 94, no. 2 (2008), 302-350.

Z. Mesyan, J. Mitchell, and Y. Péresse, Topological transformation monoids,, 2018.

J. Pérez, and C. Uzcátegui, Topologies on the symmetric inverse semigroup, Semigroup Forum 104 (2022), 398-414.

C. Rosendal, Automatic continuity of group homomorphisms, Bull. Symbolic Logic 15, no. 2 (2009), 184-214.

C. Rosendal, and S. Solecki, Automatic continuity of homomorphisms and fixed points on metric compacta, Israel J. Math. 162 (2007), 349-371.

M. Sabok, Automatic continuity for isometry groups, J. Inst. Math. Jussieu 18, no. 3 (2019), 561-590.

C. Uzcátegui-Aylwin, Ideals on countable sets: a survey with questions, Rev. Integr. temas mat. 37, no. 1 (2019), 167-198.




How to Cite

K. . Arana, J. . Pérez, and C. Uzcátegui, “Pettis property for Polish inverse semigroups”, Appl. Gen. Topol., vol. 24, no. 2, pp. 455–467, Oct. 2023.



Regular Articles