The Gateway to Computer Science Excellence
+2 votes
169 views

Let $d(x, y)$ be the usual Euclidean metric on $\mathbb{R}^{2}$. Which of the following metric spaces is complete?

  1. $\mathbb{Q}^{2}\subset\mathbb{R}^{2}$ with the metric $d(x, y)$.
  2. $[0, 1]\times [0, \infty)\subset \mathbb{R}^{2}$ with the metric $d'(x, y)=\frac{d(x, y)}{1+d(x, y)}$.
  3. $(0, \infty)\times [0, \infty) \subset \mathbb{R}^{2}$ with the metric $d(x, y)$.
  4. $[0, 1]\times [0, 1) \subset \mathbb{R}^{2}$ with the metric $d''(x, y) = \min \left \{ 1, d(x, y) \right \}$.
in Linear Algebra by Boss (29.9k points) | 169 views

Please log in or register to answer this question.

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,650 questions
56,242 answers
194,294 comments
95,950 users