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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Given a dense linear order $A$ and a countable dense linear order $B$ such that $B \subseteq A$, a $B$-indexed locator for an element $c \in A$ is an element of the indexed cartesian product of the family of functions
indexed by the cartesian product set $B \times B$
where $]a,b[$, $]a,c[$, $]c,b[$ are open intervals in $A$.
A locator is equivalent to having the structure of a Cauchy sequence with modulus of convergence. This is stronger than merely being a modulated Cauchy real number.
That every Dedekind real number has a $\mathbb{Q}$-indexed locator implies the weak limited principle of omniscience.
Last revised on June 9, 2022 at 22:39:21. See the history of this page for a list of all contributions to it.