Real Analysis

timer Asked: Oct 27th, 2015

Question description

Fix a subset S⊂R^n, and consider the characteristic function Xs: R^n → R.

a) What is the value Xs(p) got any given p∈R^n

b) Define precisely in terms of ε's and δ's what it means for Xs to be discontinuous at p∈R^n.

c) Prove that Xs is discontinuous at every boundary point of S.

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