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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Let $\mathbb{Q}$ be the rational numbers and let
be the positive rational numbers. Let $S$ be a Booij premetric space, and let $x:I \to S$ be a net with index set $I$. A $I$-modulus of convergence is a function $M \in {\mathbb{Q}_{+}} \to I$ such that for all positive rational numbers $\epsilon$ and all indices $i \in I$ and $j \in I$, if $i \geq M(\epsilon)$ and $j \geq M(\epsilon)$, then $x_i \sim_{\epsilon} x_j$.
The composition $x \circ M$ of a net $x$ and a modulus of convergence $M$ is also a net.
Auke B. Booij, Analysis in univalent type theory (pdf)
Univalent Foundations Project, Homotopy Type Theory – Univalent Foundations of Mathematics (2013)
Last revised on May 31, 2022 at 17:29:24. See the history of this page for a list of all contributions to it.