Let $H = \{u \in L^2(0,T) : u' \in L^2(0,T), u(T) = u(0)\}$ be the space of $H^1$ functions $u$ with $u(T) = u(0)$. How to show that this space is separable with the usual $H^1$ norm?
2026-04-24 08:10:27.1777018227
How to show this $H^1$ space is separable?
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Because it is a subspace of a separable space.