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 .
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 C. Goffman and D. Waterman, Approximately continuous transformations, Proc. Amer. Math. Soc. 12 (1961), 116121. MR 0120327 (22:11082)
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 Z. Grande, Sur les suites de fonctions approximativement continues et continues presque partout, Colloq. Math. 38 (1978), 259262. MR 0580932 (58:28342)
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 D. Mauldin, ideals and related Baire systems, Fund. Math. 71 (1971), 171177. MR 0293027 (45:2107)
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 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)
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 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
