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Continuous (Topology)**

Given topological spaces \((X,\mathcal{T}_X)\) and \((Y,\mathcal{T}_Y)\), a function \(f:X\to Y\) is called 'continuous' if whenever \(U\in Y\) is open, so is its preimage \(f^{-1}(U)\subseteq X\), i.e. \(\forall U\in\mathcal{T}_Y:f^{-1}(U)\in\mathcal{T}_X\).