Functions on finite metric spaces

Question

Is a function f from a finite metric space M to itself always continuous? I have tried proving it, but I have gotten stuck. Any help would be appreciated.

Where, exactly, did you get stuck? What definition of "continuous" are you using? — Daniel Hast, Nov 26 '13 at 18:33

score 5 · Accepted Answer · answered Nov 26 '13 at 18:35

5

Hint: If $M$ is a finite metric space, then which subsets of $M$ are open?

answered Nov 26 '13 at 18:35

Cameron Buie

102,994

2

Can I call this a discrete [sic] hint? – Brian M. Scott Nov 26 '13 at 20:11
1

Certainly, that is within your power. – Cameron Buie Nov 26 '13 at 20:14
Your pun was much better than mine.... – Cameron Buie Nov 26 '13 at 20:28
1

It occurred to me after I left the comment that a wonderful answer would be, in its entirety: HINT: Let me offer a discrete [sic] hint. – Brian M. Scott Nov 26 '13 at 20:29

Functions on finite metric spaces

1 Answers1