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Metric spaces and continuity
Metric spaces and continuity

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Learning outcomes

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.