Proposition 2.33.a

Proposition 2.33.a: $$Cl(A) = Int(A) \cup A'$$.

Comments
Consider a set in $$\mathbb{R}$$ under the usual metric consisting of a single point. This set has no interior and no limit points but it is closed so its closure is itself, an apparent contradiction to this proposition.

Ian mi 01:59, March 23, 2011 (UTC)Ian_mi

As Ian_mi shows above, this is not true as written. The proposition should read $$Cl(A)=A\cup A'$$.

baruch_shahi 00:29, March 26, 2011 (UTC -5)

But isn't this just definition 2.20 then? Tony Bruguier 03:04, March 30, 2011 (UTC)

You're right, Tony. I didn't catch that. In the past I have used a different definition of closure and proved this proposition from there.

baruch_shahi 23:50, March 29, 2011 (UTC -5)