Continuity & Uniform Continuity: Question on Solutions

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The discussion centers on the relationship between the continuity of a function f and the derived function g, defined as g(x) = inf_{x<t in D} f(t), where f is increasing on a dense set. It highlights that while the continuity of f does not guarantee the continuity of g, uniform continuity of f does ensure uniform continuity of g. The original poster is studying this topic independently, seeking to understand its implications for distribution functions in probability. There is a note that such questions are typically better suited for homework help forums, though the thread remains open for discussion. The focus remains on the mathematical properties and implications of continuity in this context.
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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?
 
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student12s said:
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?
 
I encounter this question while studying Probability by my own. It's not homework/coursework. The application is understanding properties of distribution functions.
 
student12s said:
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.
 
I apologize. It was a misunderstanding. I will post in the correct part of the forum. Thanks.
 

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