From: wingler@cis.ysu.edu (Dr. Eric Wingler)
Newsgroups: sci.math
Subject: Re: Prove of Find Counter Example
Date: 15 Feb 1995 12:54:08 GMT

Ahmed Hindawi (ahmed@ovrut.hep.upenn.edu) wrote:
: Hi:

: Let f:R -> R be a function from R into R (the set of real numbers). Prove
: or find a counter example that there exsit a dense subset of R (say A) 
: such that f restricted to A (f|A A->R) is a continuous function.

: --Ahmed
______________________________________________________________________________



This is known as Blumberg's Theorem.  Here is its statement in a more general
form:

If X is a metric Baire space, then for every real-valued function  
f : X -> Y , there is a dense subset D of X, such that f restricted to D is
continuous (on D). 

This result is due to Bradford and Goffman (Proceedings of the American 
Mathematical Society, 1960)

Eric J. Wingler
wingler@math.ysu.edu