# Tagged Questions

Intuitively, a continuous function is one where small changes of input result in correspondingly small changes of output. Use this tag for questions involving this concept. As there are many mathematical formalizations of continuity, please also use an appropriate subject tag such as (real-analysis) ...

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### Prove absolute continuity without Banach-Zarecki

Let $f$ be a real-valued continuous function of bounded variation on $[a,b]$. Suppose $f$ is absolutely continuous on $[a+\eta,b]$ for every $\eta\in(0,b-a)$. Show that $f$ is absolutely continuous on ...
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### Are continuous product projections always split?

Are continuous product projections always split? What's an example of a product projection without a continuous right inverse?
### For every interval $I$ in $\mathbb R$ , there exists a continuous surjection from $I \setminus \mathbb Q$ to $I \cap \mathbb Q$?
Is it true that for every interval (not singleton ) $I$ in $\mathbb R$ , there exists a continuous surjection $f : I \setminus \mathbb Q \to I \cap \mathbb Q$ ?
My problem is :Find the points at which the the mentioned function is continuous f(x) = \begin{cases} x & \text{if $x$ is a Rational Number} \\ -x & \text{if $x$ is not a ...