[1]

Lebesgue H., Leçons sur l’intégration et la recherche des fonctions primitives, Gauthier-Willars, 1904 Google Scholar

[2]

Jones F.B., Connected and disconnected plane sets and the functional equation *f*(*x*) + *f*(*y*) = *f*(*x* + *y*), Bull. Amer. Math. Soc., 48, 1942, 115–120 Google Scholar

[3]

Aron R.M., Gurariy V.I., Seoane-Sepúlveda J.B., Lineability and spaceability of sets of functions on ℝ, Proc. Amer. Math. Soc., 133, 2005, 3, 795–803 (electronic) Google Scholar

[4]

Aron R.M., Bernal González L., Pellegrino D.M., Seoane Sepúlveda J.B., Lineability: the search for linearity in mathematics, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2016, xix+308, 978-1-4822-9909-0 Google Scholar

[5]

Bernal-González L., Pellegrino D., Seoane-Sepúlveda J.B., Linear subsets of nonlinear sets in topological vector spaces, Bull. Amer. Math. Soc. (N.S.), 51, 2014, 1, 71–130, 0273-0979 Google Scholar

[6]

Azagra D., Muñoz-Fernández G.A., Sánchez V.M., Seoane-Sepúlveda J.B., Riemann integrability and Lebesgue measurability of the composite function, J. Math. Anal. Appl., 354, 2009, 1, 229–233, 0022-247X Google Scholar

[7]

Aron R.M., Conejero J.A., Peris A., Seoane-Sepúlveda J.B., Uncountably generated algebras of everywhere surjective functions, Bull. Belg. Math. Soc. Simon Stevin, 17, 2010, 3, 571–575, 1370-1444, MR 2731374Google Scholar

[8]

Bartoszewicz A., Bienias M., Głab S., Natkaniec T., Algebraic structures in the sets of surjective functions, J. Math. Anal. Appl., 441, 2016, 2, 574–585, 0022-247X Google Scholar

[9]

Bernal-González L., Ordóñez Cabrera M., Lineability criteria, with applications, J. Funct. Anal., 266, 2014, 6, 3997–4025Google Scholar

[10]

Cariello D., Seoane-Sepúlveda J.B., Basic sequences and spaceability in *l*_{p} spaces, J. Funct. Anal., 266, 2014, 6, 3797-3814, 0022-1236Google Scholar

[11]

Ciesielski K.C., Gámez-Merino J.L., Mazza L., Seoane-Sepúlveda J.B., Cardinal coefficients related to Surjectivity, Darboux, and Sierpiński-Zygmund maps, Proc. Amer. Math. Soc., 2016, in press Google Scholar

[12]

Conejero J.A., Jiménez-Rodríguez P., Muñoz-Fernández G.A., Seoane-Sepúlveda J.B., When the identity theorem “seems” to fail, Amer. Math. Monthly, 121, 2014, 1, 60–68, 0002-9890Google Scholar

[13]

Enflo P.H., Gurariy V.I., Seoane-Sepúlveda J.B., Some results and open questions on spaceability in function spaces, Trans. Amer. Math. Soc., 366, 2014, 2, 611–625, 0002-9947Google Scholar

[14]

Gámez-Merino J.L., Large algebraic structures inside the set of surjective functions, Bull. Belg. Math. Soc. Simon Stevin, 18, 2011, 2, 297–300 Google Scholar

[15]

Gámez-Merino J.L., Muñoz-Fernández G.A., Sánchez V.M., Seoane-Sepúlveda J.B., Sierpiński-Zygmund functions and other problems on lineability, Proc. Amer. Math. Soc., 138, 2010, 11, 3863–3876 Google Scholar

[16]

Gámez-Merino J.L., Muñoz-Fernández G.A., Seoane-Sepúlveda J.B., Lineability and additivity in ℝ^{ℝ}, J. Math. Anal. Appl., 369, 2010, 1, 265–272 Google Scholar

[17]

Gámez-Merino J.L., Muñoz-Fernández G.A., Seoane-Sepúlveda J.B., A characterization of continuity revisited, Amer. Math. Monthly, 118, 2011,2, 167-170Google Scholar

[18]

Gámez-Merino J.L., Seoane-Sepúlveda J.B., An undecidable case of lineability in ℝ^{ℝ}, J. Math. Anal. Appl., 401, 2013, 2, 959–962Google Scholar

[19]

García-Pacheco F.J., Martín M., Seoane-Sepúlveda J.B., Lineability, spaceability, and algebrability of certain subsets of function spaces, Taiwanese J. Math., 13, 2009, 4, 1257–1269, 1027-5487Google Scholar

[20]

García-Pacheco F.J., Rambla-Barreno F., Seoane-Sepúlveda J.B., **Q**-linear functions, functions with dense graph, and everywhere surjectivity, Math. Scand., 102, 2008, 1, 156–160 Google Scholar

[21]

Jiménez-Rodríguez P., Muñoz-Fernández G.A., Seoane-Sepúlveda J.B., On Weierstrass’ Monsters and lineability, Bull. Belg. Math. Soc. Simon Stevin, 20, 2013, 4, 577–586, 1370-1444Google Scholar

[22]

Muñoz-Fernández G.A., Palmberg N., Puglisi D., Seoane-Sepúlveda J.B., Lineability in subsets of measure and function spaces, Linear Algebra Appl., 428, 2008, 11-12, 2805–2812, 0024-3795Google Scholar

[23]

Seoane J.B., Chaos and lineability of pathological phenomena in analysis, Thesis (Ph.D.)–Kent State University, ProQuest LLC, Ann Arbor, MI, 2006, 139, 978-0542-78798-0 Google Scholar

[24]

Radcliffe D.G., A function that is surjective on every interval, Amer. Math. Monthly, 123, 2016, 1, 88–89 Google Scholar

[25]

Oxtoby J.C., Measure and category. A survey of the analogies between topological and measure spaces, Graduate Texts in Mathematics, Vol. 2, Springer-Verlag, New York-Berlin, 1971, viii+95 Google Scholar

[26]

Blumberg H., New properties of all real functions, Trans. Amer. Math. Soc., 82, 1922, 53–61, 3-540-16474-X Google Scholar

[27]

Sierpiński W., Zygmund A., Sur une fonction qui est discontinue sur tout ensemble de puissance du continu, Fund. Math., 4, 1923, 316–318 Google Scholar

[28]

Kharazishvili A.B., Strange functions in real analysis, Pure and Applied Mathematics (Boca Raton), 272, 2, Chapman & Hall/CRC, Boca Raton, FL, 2006, xii+415 Google Scholar

[29]

Shinoda J., Some consequences of Martin’s axiom and the negation of the continuum hypothesis, Nagoya Math. J., 49, 1973, 117–125 Google Scholar

[30]

Fremlin D.H., Consequences of Martin’s axiom, Cambridge Tracts in Mathematics, 84, Cambridge University Press, Cambridge, 1984, xii+325, 0-521-25091-9 Google Scholar

[31]

Balcerzak M., Ciesielski K., Natkaniec T., Sierpiński-Zygmund functions that are Darboux, almost continuous, or have a perfect road, Arch. Math. Logic, 37, 1997, 1, 29–35 Google Scholar

[32]

Ciesielski K., Pawlikowski J., The covering property axiom, CPA, Cambridge Tracts in Mathematics, 164, A combinatorial core of the iterated perfect set model, Cambridge University Press, Cambridge, 2004, xxii+174, 0-521-83920-3, 10.1017/CBO9780511546457 Google Scholar

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