Query the point being made in the final para. Is it about Q-linear functions, eg take a Hamel basis for R over Q, define a function by Q-linearity on the b in it, such as b/|b|, tweak to make bounded?

Charles Matthews 09:13, 19 Feb 2004 (UTC)

I don't know anything specifically about linear functions on R over Q, but I know there exist linear functions on R over R that are not f(x) = ax. My topology book mentions one discovered by F. B. Jones. Its graph is connected but not compact. CyborgTosser

I think you need to clarify that. All the conventional-sense linear functions of that kind are multiplication by constants. The ax+b functions are presumably not what you mean.

Charles Matthews 22:34, 21 Feb 2004 (UTC)

My mistake. The function I mention only satisfies superposition, which would make it linear over Q, not R. CyborgTosser

Page now amended. Charles Matthews 09:03, 11 Mar 2004 (UTC) (Funny, I could have sworn I did, yesterday, but the page history says not ... must be an edit that didn't make it to the far end ... CT has done the necessary now. Charles Matthews)