Share
Explore BrainMass

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
S.
[Please see attached PDF file for full problem].

for part (a), I think something similar to
http://planetmath.org/encyclopedia/CharacteristicFunction.html
can be used, correct?

Attachments

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.

$2.19