The class Ext of all extendable functions from R to R is the smallest among all Darboux-like classes of functions, which constitute different natural generalizations of the class of usual
continuous functions. In 2013, T. Natkaniec asked whether or not Ext is maximal algebrable, that is, whether there is or not an algebra of functions contained in Ext such that the set of generators of such algebra has cardinality 2c (where c is the cardinality of the continuum). In this talk we present a positive answer in a recent published paper [2] where the authors use a refined technique that was first implemented in [1].
[1] A. Bartoszewicz, M. Bienias, S. Glab, and T. Natkaniec, Algebraic structures in the sets of surjective functions, J. Math. Anal. Appl. 441 (2016), 574—585.
[2] K. C. Ciesielski, D. L. Rodríguez-Vidanes, and J. B. Seoane-Sepúlveda, Algebras of measurable extendable functions of maximal cardinality, Linear Algebra Appl. 565 (2019), 258—266.
