7
$\begingroup$

Can we define a particular metric ( except for discrete metric ) on any given set in which continuity implies uniform continuity ?

Thanks for any help .

  • 0
    Sorry for the inconvenience caused due to my editting2012-09-06

2 Answers 2

5

All compact metric spaces, since a continuous function on a compact metric space is uniformly continuous.

  • 0
    @Ricky I could get the whole paper. May be my institution has full access.2012-09-10
3

In all compact metric spaces continuity and uniform continuity is equivalent.