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bounded function (changes) in nLab

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Context

Analysis

analysis (differential/integral calculus, functional analysis, topology)

epsilontic analysis

infinitesimal analysis

computable analysis

Introduction

Basic concepts

triangle inequality

metric space, normed vector space

open ball, open subset, neighbourhood

metric topology

sequence, net

convergence, limit of a sequence

compactness, sequential compactness

differentiation, integration

topological vector space

Basic facts

continuous metric space valued function on compact metric space is uniformly continuous

…

Theorems

intermediate value theorem

extreme value theorem

Heine-Borel theorem

…

Contents

  • Idea
  • Related concepts

Idea

A function to a metric space is bounded if its image is a bounded subset.

More generally there is a concept of bounded function between bornological sets.

Related concepts

  • extreme value theorem

    extreme value theorem

  • rapidly decreasing function

  • continuous function, differentiable function, smooth function

  • integrable function, square-integrable function

  • bounded function

  • compactly supported function

  • measurable function

Last revised on November 2, 2017 at 19:38:53. See the history of this page for a list of all contributions to it.

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