Definition talk:Limit Point/Topology/Set

Some solution to the ugliness of the headings of this page needs to be invented. I am getting more motivated to really start developing a PW extension for MediaWiki, in order to achieve that transclusions are able to adapt heading levels... Now that would be great. --Lord_Farin 09:24, 24 February 2012 (EST)


 * What ugliness? --prime mover 16:12, 24 February 2012 (EST)


 * Unnecessary headings which deviate from house style to be able to transclude the page nicely. There might come instances where a workaround like this might not be feasible. I would ideally produce a structure such that one could do the following:

Pagename


 * which would transclude the proof (indicated by a custom 'proof' tag) of the page. More options could be added to the 'transclude' tag to allow for a flexible environment making transclusion more consistent and insightful (rather than littered 'onlyinclude' tags in pages, of which one has a hard time finding the use). --Lord_Farin 17:17, 24 February 2012 (EST)


 * Okay then, that would be of benefit. I admit to having had trouble in the past squeezing the information into the supported structures. --prime mover 17:37, 24 February 2012 (EST)

Incorrect definition?
I seriously doubt that the "definition by sequences" is actually equivalent to the other definitions. For example, let $\omega_1$ denote the smallest uncountable ordinal, i.e., the Hartogs number of $\omega = \left\{{0, 1, 2, \ldots}\right\}$. Consider its successor set $\omega_1^{+} = \omega_1 \cup \left\{{\omega_1}\right\}$ with its order topology. Then $\omega_1 \in \omega_1^{+}$ is a limit point of $\omega_1 \subseteq \omega_1^{+}$, but does not satisfy Definition:Limit Point of Set. --abcxyz (talk) 04:01, 12 October 2012 (UTC)