Real Analysis II

A set which has a metric in it is called

• Metric space

• Complete space

• Complete metric space

• None of these

• True

• False

Any subset of a discrete metric space is

• Bounded

• Open

• Closed

• Complete

True or False: 1.    Any set M can have a metric in it

• True

• False

True or False: 1.    Any closed interval is bounded in R

• True

• False

Every open ball in R is of the form

• (a, b)

• [a, b)

• (a, b]

• None of these

Interior of (1, 1) is

• {1}

• (1, 1)

• Empty set

• None of these

Which of the following is true?

True or False: 1.    For every distinct points x, y, there always exists disjoint open sets containing x and y respectively

• True

• False

In R with usual metric, B(1, 1) =

• [1, 1]

• (-1, 1)

• (-2, 0)

• (0, 2)