What is "subspace topology"

n. (context topology English) The topology of a subset ''S'' of a topological space ''X'' which is obtained by considering any subset of ''S'' to be an open set if it corresponds to the intersection of ''S'' with some open set of ''X''.

In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).