Definition talk:Closure (Topology)

In this case, I can't see how there is merit for two separate pages. The derived set $H'$ of $H$ is defined as the set of all limit points of $H$. Comments? --abcxyz (talk) 01:11, 16 November 2012 (UTC)


 * Someone who does not connect those two facts may not realise the two things are the same till it's pointed out in a page demonstrating their equivalence. --prime mover (talk) 06:32, 16 November 2012 (UTC)


 * Last Tuesday, a second-year student told me he had learned that $\Z_n \cong \Z / n \Z$ (through an isomorphism theorem), to which statement I looked at him in utter confusion, incapable of comprehending any more why such a statement would require a proof... It's hard to imagine not knowing such things when one in fact does. --Lord_Farin (talk) 12:04, 16 November 2012 (UTC)


 * Sorry, but I still don't get it. Anyone who follows the link to Definition:Derived Set will surely see the connection, no? --abcxyz (talk) 16:23, 16 November 2012 (UTC)


 * Now that I've actually bothered to look at the page, I agree with abcxyz that this is artificial separation of definitions. They can be merged, derived set mentioned, and we'll be done with it, on to more important/interesting stuff. --Lord_Farin (talk) 16:25, 16 November 2012 (UTC)


 * Give me a break, I'm not the one quibbling here. --prime mover (talk) 19:07, 16 November 2012 (UTC)

Rewrite thoughts: The current choice of definition 1 is unfortunate. The most important definitions, I think, are: --Dfeuer (talk) 23:29, 27 February 2013 (UTC)
 * Definition 2: the intersection of containing closed sets
 * Definition 3: the smallest containing closed set
 * Definition .... NOT HERE: the set of all adherent points of the set.


 * Another one that's missing is that the closure is the complement of the interior of the complement. --Dfeuer (talk) 23:53, 27 February 2013 (UTC)