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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
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Set of discontinuities for Thomae's function in $\mathbb{R}^2$
For this question, label:
Part A: Is $f(x,y)$ integrable? Question $3$-$7$ from Spivak's Calculus on Manifolds
Part B: Prove $f:[0,1]\times[0,1]→\mathbb{R}$ is integrable.
For part A and B question, …