Monico (2024) · Lemma 3.3

Set-Set Separator

See how \(\mathcal{N}_3\) separates two disjoint closed sets \(A\) and \(B\).

Lemma 3.3: Let \(A, B \subset K\) be disjoint closed sets. For each \(\varepsilon > 0\), there exists \(H \in \mathcal{N}_3^\sigma\) with \(0 \le H < \varepsilon\) on \(B\) and \(1-\varepsilon < H \le 1\) on \(A\). The construction iterates Lemma 3.2 over points of \(A\).
max H on B
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min H on A
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Network class
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Preset configurations
Parameters
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Layer counting
N₂ \(g_{\mathbf{a}} = 1 - \widetilde{g}_{\mathbf{a}}\)
N₂ˢ \(\sigma(s + t g_{\mathbf{a}_j})\)
N₃ \(h = \sum \sigma(s + t g_{\mathbf{a}_j})\)
N₃ˢ \(H = \sigma(s' + t' h)\)