Exercise 3. [Closure in metric space] Let (X, d) be a metric space and Y be a nonempty subset of X. The distance of a point ze X from the subset Y is a function X → [0, +∞[ defined by d(x, y) = inf{d(x, y); y € Y}. 1. Verify that the distance function is well defined. 2. Prove that Y= {re X;d(x, y)=0}.
Exercise 3. [Closure in metric space] Let (X, d) be a metric space and Y be a nonempty subset of X. The distance of a point ze X from the subset Y is a function X → [0, +∞[ defined by d(x, y) = inf{d(x, y); y € Y}. 1. Verify that the distance function is well defined. 2. Prove that Y= {re X;d(x, y)=0}.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
Related questions
Question
topolgy exercice 3
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage