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A Separately Continuous Function Not Somewhat Continuous


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We construct a separately continuous function f : ℚ × ℚ → [0; 1] and a dense subset D ⊆ ℚ × ℚ such that f[D] is not dense in f[ℚ × ℚ], in other words, f is separately continuous and not somewhat (feebly) continuous.

eISSN:
2391-4238
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Mathematics, General Mathematics