Purchase Solution

Metric Spaces

Not what you're looking for?

Ask Custom Question

Give an example of each of the following:

a) an infinite subset of R with no cluster point
b) a complete metric space that is bounded but not compact
c) a metric space none of whose closed balls is complete

Purchase this Solution

Solution Summary

This solution explains how to solve the given problems involving Metric Spaces.

Solution Preview

a) We consider the integer set Z in R. Z has no cluster point.
Because for any integer n in Z, we consider its neighborhood (n - 0.5, n + 0.5). In this neighborhood, there does not exist another point in Z.

b) For the real set R, we consider the discrete metric d with d(x, y) = 1 if x is not equal to y and d(x, x) = 0.
Then R is ...

Purchase this Solution


Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability