Let \((X,\tau)\) be a topological space . We define the subspace topology for a subset \(S\subset X\) by declaring \(V\subset S\) open if an open set \(U\in \tau\) exists such that \(V=U\cap S\). In this case, \(S\) is called subspace.
Remarks
Let \((X,\tau)\) be a topological space . We define the subspace topology for a subset \(S\subset X\) by declaring \(V\subset S\) open if an open set \(U\in \tau\) exists such that \(V=U\cap S\). In this case, \(S\) is called subspace.