Connectedness in the Pluri-fine Topology
| dc.creator | Marzguioui, Said El | |
| dc.creator | Wiegerinck, Jan | |
| dc.date | 2008-01-30 | |
| dc.date.accessioned | 2026-07-07T08:57:17Z | |
| dc.date.available | 2026-07-07T08:57:17Z | |
| dc.description | We study connectedness in the pluri-fine topology on $\CC^n$ and obtain the following results. If $Ω$ is a pluri-finely open and pluri-finely connected set in $\CC^n$ and $E\subset\CC^n$ is pluripolar, then $Ω\setminus E$ is pluri-finely connected. The proof hinges on precise information about the structure of open sets in the pluri-fine topology: Let $Ω$ be a pluri-finely open subset of $\CC^{n}$. If $z$ is any point in $Ω$, and $L$ is a complex line passing through $z$, then obviously $Ω\cap L$ is a finely open neighborhood of $z$ in $L$. Now let $C_L$ denote the finely connected component of $z$ in $Ω\cap L$. Then $\cup_{L\ni z} C_L$ is a pluri-finely connected neighborhood of $z$. As a consequence we find that if $v$ is a finely plurisubharmonic function defined on a pluri-finely connected pluri-finely open set, then $v= -\infty$ on a pluri-finely open subset implies $v\equiv -\infty$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0801.4652 | |
| dc.identifier | http://arxiv.org/abs/0801.4652 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146907 | |
| dc.subject | Complex Variables | |
| dc.subject | 32U15, 31C40, 32U05, 30C85 | |
| dc.title | Connectedness in the Pluri-fine Topology | |
| dc.type | text |