Timeline for Regarding graphs of continuous functions between zero dimensional spaces
Current License: CC BY-SA 3.0
6 events
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| May 4, 2014 at 13:44 | history | edited | Partha Pratim Ghosh | CC BY-SA 3.0 |
added 862 characters in body
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| Apr 30, 2014 at 17:44 | comment | added | Partha Pratim Ghosh | Also, I could not follow the proof of your statement; could you please provide a proof? | |
| Apr 30, 2014 at 17:43 | comment | added | Partha Pratim Ghosh | Thanks Ramiro, however, if one takes the identity map on $I(B)$, then also $P$ and $G$ are homeomorphic; in particular, if $B$ were zero dimensional then its identity map is such a case. But then $f$ is not constant, and neither does every open subset become closed. | |
| Apr 30, 2014 at 16:53 | comment | added | Ramiro de la Vega | If $f$ is constant then both $P$ and $G$ are homeomorphic to $X$. Thus $I(P)$ and $G$ are homeomorphic only if $X$ is such that every open set is closed. In the $T_0$ case this means that $X$ is discrete. | |
| Apr 30, 2014 at 14:21 | review | First posts | |||
| Apr 30, 2014 at 14:46 | |||||
| Apr 30, 2014 at 14:04 | history | asked | Partha Pratim Ghosh | CC BY-SA 3.0 |