I and my friends confused with this statement "a function $f:X\to Y$ is not countably continuous." Does it mean that the set of discontinuities of $f$ is countable?
a function is not countably continuous
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real-analysis
continuity
1 Answers
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I suppose that the definition is :
For $X\subset \mathbb{R}$ a function $f:X\to \mathbb{R}$ is countably continuous if there is a countable cover $\{X_n, n \in \mathbb{N}\}$ of $X$ such that each restriction $f|X_n$ is continuous.
that you can find, e.g., here. And this means that the set of discontinuities is countable.
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0Novanti: Does the definition still hold for any space $X, Y$? – 2017-01-26
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0Yes, I think that the definition can still hold, but I've not a reference. – 2017-01-26