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We discussed the following on 9/22/16:

(1) What are the dimensions of and ?

(2) Let be a subset of . Show that the set of limit points of , , is closed.

A student gave an for problem (2) which works fine if is a closed set (it depended on the fact that ).

[A student pointed out that I used a definition for limit point which was different from (but also equivalent to) that given in the text. We've replaced any usage of the definition I originally used with the text's definition. We also discussed why the two definitions are equivalent in the Thursday tutorial that took place on 9/29/16.]

Let be given and let be given.

Then there is some such that

There is also a point such that


That is,