Continuity & Uniform Continuity: Question on Solutions

[student12s]

I´ve been trying to solve this for some time: Let f: R to R be an increasing on a dense set. Define g(x)=inf_{x<t in D} f(t). Show that continuity of f does not imply continuity of g but uniform continuity of f does imply uniform continuity of g.
Any help?

 

[berkeman]

I´ve been trying to solve this for some time: Let f: R to R be an increasing on a dense set. Define g(x)=inf_{x<t in D} f(t). Show that continuity of f does not imply continuity of g but uniform continuity of f does imply uniform continuity of g.
Any help?

Is this homework/coursework? If not, what is the application?

 

[student12s]

I encounter this question while studying Probability by my own. It's not homework/coursework. The application is understanding properties of distribution functions.

 

[berkeman]

I encounter this question while studying Probability by my own. It's not homework/coursework. The application is understanding properties of distribution functions.

In general, even self-study questions should go into the Homework Help forums. Please keep that in mind. I'll leave this thread here for now, however.

 

[student12s]

I apologize. It was a misunderstanding. I will post in the correct part of the forum. Thanks.