After studying this course, you should be able to:
understand the Euclidean distance function on Rn and appreciate its properties, and state and use the Triangle and Reverse Triangle Inequalities for the Euclidean distance function on Rn
explain the definition of continuity for functions from Rn to Rm and determine whether a given function from Rn to Rm is continuous
explain the geometric meaning of each of the metric space properties (M1) – (M3) and be able to verify whether a given distance function is a metric
distinguish between open and closed balls in a metric space and be able to determine them for given metric spaces
define convergence for sequences in a metric space and determine whether a given sequence in a metric space converges
state the definition of continuity of a function between two metric spaces.