A set E in a metric space is called clopen

A set E in a metric space is called clopen if it is both open and closed.
a) Prove that every metric space has at least two clopen sets.
b) Prove that a metric space is connected if and only if it contains exactly two clopen sets.

Members

  • Access to 2 Million+ Textbook solutions
  • Ask any question from 24/7 available
    Tutors
$9.99
VIEW SOLUTION

OR

Non-Members

Get help from Numerical Analysis Tutors
Ask questions directly from Qualified Online Numerical Analysis Tutors .
Best for online homework assistance.