30 Mar
2000
30 Mar
'00
1:32 a.m.
It is not even true for additive functions. Take a Hamel base and send every element of the base to 1. On Wed, 29 Mar 2000, Peter Freyd wrote:
M.M. Mawanda asks:
I have been asked the following question: Is it true that any function defined in a real number closed interval [a,b] (there is not a hypothesis of continuity) is bounded in an open subinterval (c,d) of [a,b]? My spontaneous was NO. Unfortunately I cannot find a counter-example to disapproved my answer. Can someone help.
No it is not true. For example, the function defined by:
f(x) = if x is irrational then 0 else if x = p/q where p and q are co-prime then q.