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