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< strongly extensional function
Given a sequentially Cauchy complete Archimedean ordered field $\mathbb{R}$, a function $f:\mathbb{R} \to \mathbb{R}$ is strongly extensional if for every $x:\mathbb{R}$ and $y:\mathbb{R}$, $\vert f(x) - f(y) \vert \gt 0$ implies that $\vert x - y \vert \gt 0$.
In particular, this definition applies to Dedekind real numbers, which is used for proving Brouwer's theorem? in real-cohesive homotopy type theory.
Brouwer's theorem?
Last revised on June 14, 2022 at 20:18:21. See the history of this page for a list of all contributions to it.