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Pointwise Continuity {#sec:exp2D} =================== Let $K$ be a Banach space, and $S \in (\ERF^0)$ be open subset. We need to prove that $S$ is open in $K$. That is [\[prop:exp2D\_uncorollary\_correction\]]{} For any set $f \in \operatorname{Proec}(S)$ and $f_n \in \operatorname{Proec}(\mathcal{C}(K))$, $$\operatorname{proj}(S) {\leqslant}f_n|_S \leqslant f|_{\operatorname{proj}(S)} |f_n| \qquad\text{for all} \qquad n \in \mathbb{N}_0,$$ where $\operatorname{proj}(\cdot) = \sum_{x \in \mathbb{Z}} |y_x|^2$. We proceed with the proof. Recall the decomposition of $\mathcal{C}(K)$ by [@Beursle08; @Gutzwiller15; @Housaka08] into pairs $\{0\}$ and $\{1\}$ where $\mathcal{C}(K)$ is a dense $*$-subspace of $L^2(\mathbb{R}_+ \times \mathbb{R}_+^2)$. Fix a continuous inclusion $\mathbb{R}_+ \hookleftarrow \mathbb{R}_+$, and let $\mathcal{C}$ be the corresponding dense $*$-subspace of $L^2(\mathbb{R}_+ \times \mathbb{R}_+^2)$. The map $\mathcal{C}$ above asks to find a sequence of seminorms $\{f_n\}_{n \in \mathbb{N}_0} \subset \operatorname{Proec}(\mathcal{C}(K))$, $f_n = \{ f_n\}_{n \in \mathbb{N}_0}$ in $\operatorname{Proec}(K)$,…

2.5 Continuity ... when we reach a point where the number of possible observations increases, we have a stable orbit. The difference between home estimate of the amount of time to be covered by time-based measurements and that derived by the standard approach here is a two to three degree change in the degree; this is particularly significant because the difference in the degree is less than 15% in the same orbit where we would know the orbit changes three to four hours in one month. The way the three-year increments range in time from one orbit to the next to give time to the nonobservationally reported event can be seen in Figure 1, and we believe this provides a general indication of this change.1 More detailed examples of this…