TITLE: Why is $(.5, 1]$ considered an open set in $[0, 1]$?
QUESTION [6 upvotes]: Why is $(.5, 1]$ considered an open set in $[0, 1]$? This is from a topology textbook.

REPLY [2 votes]: If you think of $[0,1]$ as a metric space, with the usual metric restricted to it, then your set is the open ball (in the metric space $[0,1]$) of radius $0.5$ with center $1$.  Open balls are open sets.