x_{1} (metric space/set/class/structure) is a metric subspace/subset(/subclass) of x_{2} (metric space/set/class) which is closed therein. x_{1} is an closed subset of x_{2}, where closedness is taken to be understood as being considered within x_{2} and under the metric shared by x_{1} and x_{2}

In x_{2}, x_{1} is composed exactly of members which are limit points of x_{1}. Confer: sezrurkle.