Talk:Closure Equals Union with Derivative

This page matches the definition as given here: Definition:Closure (Topology)/Definition 1:

The closure of $H$ (in $T$) is defined as:

$H^- := H \cup H'$

where $H'$ is the derived set of $H$.

Then we have:

The derived set of $X$ is the set of all limit points of $X$.

It is often denoted $X'$.

This is differently defined from:

The derivative of $A$ in $T$ is the set of all accumulation points of $A$.

... unless it can be resolved that what is defined here as an "accumulation point" is the same thing as a "limit point".

The difference between "accumulation point" and "Limit point" is subtle, and many texts do not make that distinction. I suspect that some texts which do mention "accumulation point" actually mean "limit point". Care is needed here. --prime mover (talk) 14:30, 19 December 2015 (UTC)