On Feb 5, 4:33 am, "T.H. Ray" <thray...@aol.com> wrote: > Ostap Bender wrote > > On Feb 3, 3:48 am, "T.H. Ray" <thray...@aol.com> > > wrote: > > > > Brouwer, who gave us the fixed point theorem, also > > > gave us the deeper result: all real functions are > > continuous. > > > Excuse me? What do you mean by "real functions"? > > Functions in the range of the real numbers. >
And what is the domain? Reals? An arbitrary topological space? A singleton?
Are you saying that all functions f: R -> R are continuous? And that Brouwer proved this? I would be willing pay big money to see a proof of that.