So I have an exam in Real Analysis I coming up next week and I was hoping if someone can help me out.(adsbygoogle = window.adsbygoogle || []).push({});

I hope my question makes sense because I think I might be confused with defining the metric space or so...

1. The problem statement, all variables and given/known data

a)Suppose that we have a metric space M with the discrete metric

d(x,y) = 1 if x = y

d(x,y) = 0 if x =/= y

Is this open or closed?

b)Suppose that we are in R (the real line) and the metric is define as

d(x,y) = 1 if x = y

d(x,y) = 0 if x =/= y

Is this open or closed?

2. Relevant equations

Definition:

A set is Yopenif every point in Y is aninterior point

A set is Yclosedif every point in Y is anlimit point

3. The attempt at a solution

a)Im not even sure if question a makes sense because I didn't define the metric.

b) I'm pretty sure it is open and closed because both the definitions work.

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# Real Analysis -Open/Closed sets of Metric Spaces

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