nLab modulated Cauchy complete space

Redirected from "sequentially modulated Cauchy complete".
Contents

Context

Analysis

Constructivism, Realizability, Computability

Contents

Idea

A notion of Cauchy space where only certain Cauchy nets with a particular modulus of convergence converges in the space.

Definition

Let SS be a Cauchy space (such as a uniform space or a metric space). Given a directed set II, SS is II-modulated Cauchy complete if every Cauchy net in SS with index set II and with a II-modulus of convergence converges.

A Cauchy space is said to be sequentially modulated Cauchy complete if every Cauchy sequence in SS with a \mathbb{N}-modulus of convergence converges.

Examples

See also

Created on May 6, 2022 at 17:28:13. See the history of this page for a list of all contributions to it.