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Characteristic Function of Metric Space

Let S ⊂ M.
(a) Define the characteristic function Xs : M --> R.
(b) If M is a metric space, show that Xs(x) is discontinuous at x if and only if x is a boundary point of
[Please see attached PDF file for full problem].

for part (a), I think something similar to
can be used, correct?


Solution Summary

Characteristic function of a metric space is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.