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| For a state-dependent differential delay equation $\dot{u}(t) = F(u_t), \, u_0=\varphi \in C, $ in a general Banach state space $X$ and initial-history space $C=C([-r,0];X),$ and closed subsets $\hat{X}$ of $X,$ and $\hat{C}$ of $C,$ we discuss a subtangential condition in terms of $F,$ $\hat{X}$ and $\hat{C}$ ensuring flow invariance of $\hat{X}$ for solutions to the equation, and of $\hat{C}$ for their history-segments, with $F$ almost locally Lipschitzian, and a differentiability assumption on $F$ common in this context. |
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