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Products of quasi-continuous functions. (English) Zbl 0755.26002
The following theorem is proved: A cliquish function \(h:R\to R\) is the product of \(n\) quasi-continuous functions iff each of the sets \(\{x:h(x)=0\}\), \(\{x:h(x)<0\}\), \(\{x:h(x)>0\}\) is the union of an open set and a nowhere dense set. Moreover, if \(h\) is Lebesgue measurable (resp. of the Baire class \(\alpha)\), then the factors can be taken to be Lebesgue measurable (resp. of the Baire class \(\alpha)\).

MSC:
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A30 Singular functions, Cantor functions, functions with other special properties
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References:
[1] BLEDSOE W. W.: Neighbourly functions. Proc. Amer. Math. Soc. 3, 1952, 114-115. · Zbl 0046.40301 · doi:10.2307/2032465
[2] GRANDE Z.: Sur les functions cliquish. Časop. Pěst. Mat. 110, 1985, 225-236. · Zbl 0579.54009 · eudml:21592
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