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Show that the topologies of R_{l}(which is the lower limit topology) and then.... R_{K}(which is the set of all numbers of the form 1/n, for n E [tex]Z[/tex]_{+}meaning that they are all 1/n for all the positive integers)

So i can compare this to the standard topology which is...

Given a basis element (a,b) for the standard topology (i will call this T) and a point x of (a,b), the basis element [x,b)for R_{l}contains x and lies in (a,b). ON the other hand, given the basis element [x,b) for R_{l}there is no open interval (a,b) that contians x and lies in [x,d). Thus R_{l}is strictly finer than T.

same applies to R_{k}.

Given a basis element (a,b) for the standard topology (i will call this T) and a point x of (a,b), the basis element for R_{k}contains x. ON the other hand, given the basis element B=(-1,2) - K for R_{k}and the point 0 of B, There is no open interval that contains 0 and lies in B.

I don't know how i can compare the two together... i might be like blind... and that i might be right under my nose... but still.. i'm struggling.

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# Comparing topologies

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