Subspace topology
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Definition
We define the subspace topology as follows.
Given a topological space [math](X,\mathcal{J})[/math] and any [math]Y\subset X[/math] we can define a topology on [math]Y,\ (Y,\mathcal{J}_Y)[/math] where [math]\mathcal{J}_Y=\{Y\cap U|U\in\mathcal{J}\}[/math]
We may say "[math]Y[/math] is a subspace of [math]X[/math] (or indeed [math](X,\mathcal{J})[/math]" to implicitly mean this topology.
