- #1
workerant
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Suppose f:[a,b]--> R and g:[a,b]-->R. Let T={x:f(x)=g(x)}
Prove that T is closed.
I know that a closed set is one which contains all of its accumulation points. I know that f and g must be uniformly continuous since they have compact domains, that is, closed and bounded domains. Now T is the set for which f(x)=g(x), so it seems pretty obvious that this set is going to be closed, but I don't really know how to actually prove this.
Prove that T is closed.
I know that a closed set is one which contains all of its accumulation points. I know that f and g must be uniformly continuous since they have compact domains, that is, closed and bounded domains. Now T is the set for which f(x)=g(x), so it seems pretty obvious that this set is going to be closed, but I don't really know how to actually prove this.