Timeline for Existence of an arbitrary Small positive continuous real Valued Function

10 events

when toggle format	what		by	license	comment
Jun 21, 2012 at 6:44	vote	accept	Ali Reza
Jun 20, 2012 at 16:16	answer	added	Joseph Van Name		timeline score: 1
Jun 20, 2012 at 13:30	answer	added	Pietro Majer		timeline score: 2
Jun 19, 2012 at 23:48	answer	added	François G. Dorais		timeline score: 5
Jun 19, 2012 at 23:08	answer	added	user24527		timeline score: 0
Jun 19, 2012 at 22:24	comment	added	Andreas Blass		Gerald Edgar's example easily generalizes to show that the zero-set of any continuous real-valued function on $X$ would have to be open. Thus, all continuous functions from $X$ to $\mathbb R$ have to be locally constant.
Jun 19, 2012 at 19:33	history	edited	Ali Reza	CC BY-SA 3.0	added 492 characters in body; deleted 8 characters in body
Jun 19, 2012 at 19:20	comment	added	Ali Reza		Thanks Dear Edgar. But I think I forgot to pose the important part of my Question. For this I must apologize from members of "MO". I will fixe it.
Jun 19, 2012 at 19:12	comment	added	Gerald Edgar		Inn general, no. Say $X$ is the real line, $\epsilon_x=x$ for $x \ne 0$ and $\epsilon_0=1$.
Jun 19, 2012 at 18:45	history	asked	Ali Reza	CC BY-SA 3.0