transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
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 way of defining a dense linear order that behaves like the closed intervals in a dense linear order, which identifies each closed interval $[a,b]$ with the pair of open intervals $(-\infty, a), (b, \infty)$.
Given a DLO $D$, An interval cut is a pair $(L,U)$ of subsets of elements in $D$ satisfying these conditions:
The DLO of closed intervals in $D$ is defined to be the set of all interval cuts in $D$.
The set of all located interval cuts in $\mathbb{Q}$ is the Dedekind real numbers
The set of all interval cuts in $\mathbb{Q}$ with a locator is the modulated Cauchy real numbers
Auke Booij, Extensional constructive real analysis via locators, (abs:1805.06781)
Mark Bridger, Real Analysis: A Constructive Approach Through Interval Arithmetic, Pure and Applied Undergraduate Texts 38, American Mathematical Society, 2019.
Created on May 6, 2022 at 14:46:01. See the history of this page for a list of all contributions to it.