The role of counterexamples in understanding the closed graph and composition theorems

We present 2 theorems and 20 counterexamples illustrating the surprising behaviour of functions between metric spaces.

Authors

Simon Reinwand (ORCID: https://orcid.org/0000-0003-1447-711X)
Jürgen Appell

Publication Details

Journal: Examples and Counterexamples
Published: 2025-02-04
DOI: https://doi.org/10.1016/j.exco.2025.100177
Primary Topic: Algebraic and Geometric Analysis
Type: article
Field-Weighted Citation Impact: 0.00

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article

The role of counterexamples in understanding the closed graph and composition theorems

Simon Reinwand, Jürgen Appell

Feb 4, 2025

Examples and Counterexamples

Algebraic and Geometric Analysis

article

The role of counterexamples in understanding the closed graph and composition theorems

Simon Reinwand, Jürgen Appell

February 4, 2025article en

Abstract

We present 2 theorems and 20 counterexamples illustrating the surprising behaviour of functions between metric spaces.

Examples and CounterexamplesVol. 7

Openalex Percentile: Top 97%

Algebraic and Geometric Analysis

DOI Open Access PDF OpenAlex

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The role of counterexamples in understanding the closed graph and composition theorems — Simon Reinwand, Jürgen Appell · Examples and Counterexamples (2025) | TGRS Research Map | TGRS