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So I'm looking at this proof, which is presented as a problem in Gamelin & Greene but I'm having some trouble understanding it.

http://www.math.ru.nl/~vangool/teach/top/sorgenfreyplaneisnotnormal.pdf

Part (a), (b) and (c) are straightforward enough. However I'm having trouble following his reasoning on (d). I understood how everything is defined, I just don't see how the Baire Category Theorem applies, which says that the intersection of an infinite sequence of dense subsets of a complete metric space is dense. Could someone please explain it further?

  • 0
    Can I ask what is the $J_\delta(t_m)$ in d)?2012-10-09
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    You believe that the Baire Category Theorem applies to $\mathbb{R}$, right? And that a set dense in the Sorgenfrey topology is also dense in the regular topology?2012-10-09

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