Basic Analysis I — Real Analysis · Problem 7.1.4

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · metric-spaces

Problem

Let the set

X \coloneq \{A, B, C\}

represent 3 buildings on campus. Suppose we wish our distance to be the time it takes to walk from one building to the other. It takes 5 minutes either way between buildings

A

and

B

. However, building

C

is on a hill and it takes 10 minutes from

A

and 15 minutes from

B

to get to

C

. On the other hand it takes 5 minutes to go from

C

A

and 7 minutes to go from

C

B

, as we are going downhill. Do these distances define a metric? If so, prove it, if not, say why not.

Related theory

metric-spaces

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