Classes of Baire functions
Authors:
Gregory V. Cox and Paul D. Humke
Journal:
Trans. Amer. Math. Soc. 269 (1982), 627635
MSC:
Primary 26A21
MathSciNet review:
637714
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Abstract: Let and denote the sets of approximately continuous and almost everywhere continuous functions, and denote Baire's first class generated by . The classes , , , and Grande's class are investigated in some detail. Although Grande's question of whether is not settled, we do show, among other results, that .
 [CH]
G.
V. Cox and P.
D. Humke, A note on pointwise limits of functions which are
approximately continuous and almost everywhere continuous, Studia Sci.
Math. Hungar. 14 (1979), no. 4, 319–323. MR 685898
(84g:26002)
 [GW]
Casper
Goffman and Daniel
Waterman, Approximately continuous
transformations, Proc. Amer. Math. Soc. 12 (1961), 116–121.
MR
0120327 (22 #11082), http://dx.doi.org/10.1090/S00029939196101203276
 [G]
Zbigniew
Grande, Sur les suites de fonctions approximativement continues et
continues presque partout, Colloq. Math. 38
(1977/78), no. 2, 259–262 (French). MR 0580932
(58 #28342)
 [K]
K.
Kuratowski, Topology. Vol. I, New edition, revised and
augmented. Translated from the French by J. Jaworowski, Academic Press, New
York, 1966. MR
0217751 (36 #840)
 [M]
R.
Daniel Mauldin, 𝜎ideals and related Baire systems,
Fund. Math. 71 (1971), no. 2, 171–177. MR 0293027
(45 #2107)
 [N]
T. Nishiura, The topology of almost everywhere continuous, approximately continuous functions, Acta Math. (to appear).
 [O]
Richard
J. O’Malley, Approximately differentiable functions: the
𝑟 topology, Pacific J. Math. 72 (1977),
no. 1, 207–222. MR 0447499
(56 #5810)
 [O]
R.
J. O’Malley, Approximately continuous functions which are
continuous almost everywhere, Acta Math. Acad. Sci. Hungar.
33 (1979), no. 34, 395–402. MR 542489
(80g:26006), http://dx.doi.org/10.1007/BF01902575
 [P]
David
Preiss, Limits of approximately continuous functions,
Czechoslovak Math. J. 21 (96) (1971), 371–372. MR 0286947
(44 #4154)
 [CH]
 G. Cox and P. Humke, A note on pointwise limits of functions which are approximately continuous and almost everywhere continuous, Studia Sci. Math. Hungar. (to appear). MR 685898 (84g:26002)
 [GW]
 C. Goffman and D. Waterman, Approximately continuous transformations, Proc. Amer. Math. Soc. 12 (1961), 116121. MR 0120327 (22:11082)
 [G]
 Z. Grande, Sur les suites de fonctions approximativement continues et continues presque partout, Colloq. Math. 38 (1978), 259262. MR 0580932 (58:28342)
 [K]
 K. Kuratowski, Topology. I, Academic Press, New York, 1966 and PWN, Warsaw, 1958. MR 0217751 (36:840)
 [M]
 D. Mauldin, ideals and related Baire systems, Fund. Math. 71 (1971), 171177. MR 0293027 (45:2107)
 [N]
 T. Nishiura, The topology of almost everywhere continuous, approximately continuous functions, Acta Math. (to appear).
 [O]
 R. J. O'Malley, Approximately differentiable functions: the topology, Pacific J. Math. 72 (1977), 207222. MR 0447499 (56:5810)
 [O]
 , Approximately continuous functions which are continuous almost everywhere, Acta Math. Acad. Sci. Hungar. 33 (1979), 395402. MR 542489 (80g:26006)
 [P]
 D. Preiss, Limits of approximately continuous functions, Czechoslovak Math. J. 96 (1971), 371372. MR 0286947 (44:4154)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198206377148
PII:
S 00029947(1982)06377148
Keywords:
Approximately continuous,
almost everywhere continuous,
Baire function
Article copyright:
© Copyright 1982 American Mathematical Society
