Ivan Shishkin, Rye (1878)

Problems/TopologyExerciseUnreviewed

A simple homeomorphism?

by Ancient Tree·
25
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
English
EnglishFrançais
Unreviewed. This problem has not been reviewed by trusted users yet.

Let f:R→Rf:\R \rightarrow \R defined as f(x)=x+3f(x)=x+3. Is it an homeomorphism?

I solved itMark it doneAdd to my listKeep it in your list
I like this problem1 like

Liked by

Solutions

1
Reveal solutionsAre you sure? Give it a try first.

Solution by Anduril

Discussions0 useful votes

It is continous and its inverse is defined by g(x)=x-3 which is also continuous.

Note that expliciting an inverse proves the bijectivity.

Report

For an unclear, ambiguous, or possibly incorrect statement, please use the Discussion tab on the right. Report content that needs moderator intervention, such as dangerous, clearly non-mathematical, or plagiarized content.