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On sequences of real functions with the Darboux property. (English) Zbl 0754.26001
The authors prove the following two theorems:
1. Each pointwise discontinuous real function of a real variable is the limit of a sequence of quasi-continuous functions with the Darboux property.
2. Each real function of a real variable with the Baire property is the limit of a sequence of pointwise discontinuous functions with the Darboux property.

MSC:
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
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References:
[1] GRANDE Z.: Sur la quasi-continuité et la quasi-continuité approximative. Fund. Math. 129, 1988, 167-172. · Zbl 0657.26003
[2] GRANDE Z., SOŁTYSIK L.: Some remarks on quasi-continuous real functions. Problemy Matematiczne · Zbl 0705.26008
[3] KEMPISTY S.: Sur les fonctions quasicontinues. Fund. Math. 19, 1932, 184-197. · Zbl 0005.19802
[4] KURATOWSKI K.: Topologie I. Warszawa 1958. · Zbl 0078.14603
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