analysis (differential/integral calculus, functional analysis, topology)
metric space, normed vector space
open ball, open subset, neighbourhood
convergence, limit of a sequence
compactness, sequential compactness
continuous metric space valued function on compact metric space is uniformly continuous
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A function $f:\mathbb{R}_D \to \mathbb{R}_D$ is locally nonzero if for all Dedekind real numbers $x \lt y$, there exists a Dedekind real number $z \in \mathbb{R}_D$ with $x \lt z \lt y$ and $\vert f(z) \vert \gt 0$.
Every monotonic function on the Dedekind real numbers is locally nonzero.
Every real polynomial function apart from the zero polynomial function is locally nonzero.
Last revised on July 7, 2022 at 02:17:52. See the history of this page for a list of all contributions to it.