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rad0786
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So I have an exam in Real Analysis I coming up next week and I was hoping if someone can help me out.
I hope my question makes sense because I think I might be confused with defining the metric space or so...
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?
Definition:
A set is Y open if every point in Y is an interior point
A set is Y closed if every point in Y is an limit point
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.
I hope my question makes sense because I think I might be confused with defining the metric space or so...
Homework Statement
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?
Homework Equations
Definition:
A set is Y open if every point in Y is an interior point
A set is Y closed if every point in Y is an limit point
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.