Let be a topological space, and let . An element is said to be a limit point of if every open set containing also contains at least one point of distinct from . Note that we can often take a nested sequence of open such sets, and can thereby construct a sequence of points which converge to , partially motivating the terminology ”limit” in this case.
is a limit point of if and only if there is a net in converging to which is not residually constant.
is a limit point of if and only if there is a filter on converging (http://planetmath.org/filter) to .
If is a metric (or first countable) space, is a limit point of if and only if there is a sequence of points in converging to .
|Date of creation||2013-03-22 12:06:51|
|Last modified on||2013-03-22 12:06:51|
|Last modified by||mathcam (2727)|