From: maxkanov@math.upenn.edu (Max Kanovitch)
To: categories@mta.ca
Subject: Re: Re: stupid question?
Date: Wed, 29 Mar 2000 18:13:53 -0500 (EST) [thread overview]
Message-ID: <200003292313.SAA14643@hans.math.upenn.edu> (raw)
Dear M.M. Mawanda,
> >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]?
The real fun is about a function f such that
f is unbounded in any open interval (c,d), and
in addition to that: f(x+y) = f(x)+f(y).
> Date: Wed, 29 Mar 2000 15:23:16 -0500 (EST)
> From: Peter Freyd <pjf@saul.cis.upenn.edu>
> Subject: categories: Re: stupid question?
>
> 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.
>
next reply other threads:[~2000-03-29 23:13 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-03-29 23:13 Max Kanovitch [this message]
2000-03-30 3:00 ` Todd Wilson
-- strict thread matches above, loose matches on Subject: below --
2000-03-29 20:23 Peter Freyd
2000-03-30 1:32 ` question? Michael Barr
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