In this paper we look at various generalizations of continuity for a function and determine necessary additional conditions which result in continuity in the ordinary sense.
References
C. E. Burgess, Continuous functions and connected graphs, Amer. Math. Monthly, 97 (1990), 337–339. MR1048448 10.2307/2324521 C. E. Burgess, Continuous functions and connected graphs, Amer. Math. Monthly, 97 (1990), 337–339. MR1048448 10.2307/2324521
C. Goffman and C. J. Neugebauer, Linearly continuous function, Proc. Amer. Math. Society, 12 (1961), 997–998. MR136686 0101.04603 C. Goffman and C. J. Neugebauer, Linearly continuous function, Proc. Amer. Math. Society, 12 (1961), 997–998. MR136686 0101.04603
Z. Grande, On discrete limits of sequences of Darboux bilaterally quasicontinuous functions, Real Analysis Exch., 26 (2000–2001), 727–734. MR1844389 1024.26002 euclid.rae/1214571363
Z. Grande, On discrete limits of sequences of Darboux bilaterally quasicontinuous functions, Real Analysis Exch., 26 (2000–2001), 727–734. MR1844389 1024.26002 euclid.rae/1214571363
Z. Grande and T. Natkaniec, On quasi-continuous bijections, Acta Math. Univ. Comenianae, 60 (1991), 31–34. MR1120595 0732.26005 Z. Grande and T. Natkaniec, On quasi-continuous bijections, Acta Math. Univ. Comenianae, 60 (1991), 31–34. MR1120595 0732.26005
P. E. Long and E. E. McGehee, Jr., Properties of almost continuous functions, Proc. AMS, 24 (1970), 175–180. MR251704 0186.56003 10.1090/S0002-9939-1970-0251704-6 P. E. Long and E. E. McGehee, Jr., Properties of almost continuous functions, Proc. AMS, 24 (1970), 175–180. MR251704 0186.56003 10.1090/S0002-9939-1970-0251704-6
T. Neubrunn, Quasi-continuity, Real Anal. Exch., 14 (1988-89), 259–306. MR995972 0679.26003 T. Neubrunn, Quasi-continuity, Real Anal. Exch., 14 (1988-89), 259–306. MR995972 0679.26003
Z. Piotrowski and E. Wingler, A note on the continuity points of functions, Real Anal. Exch., 16 (1990-91), 408–414. MR1112034 0733.26006 Z. Piotrowski and E. Wingler, A note on the continuity points of functions, Real Anal. Exch., 16 (1990-91), 408–414. MR1112034 0733.26006
W. Sierpinski, Sur une propertie de fontions de deux variables reeles, continues par rapport a chacune de variables, Publ. Math. Univ. Belgrade, 1(1932), 125–128. W. Sierpinski, Sur une propertie de fontions de deux variables reeles, continues par rapport a chacune de variables, Publ. Math. Univ. Belgrade, 1(1932), 125–128.