Pervasive algebras on planar compacts

Čerych, Jan. "Pervasive algebras on planar compacts." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 491-494. <http://eudml.org/doc/248393>.

@article{Čerych1999,
abstract = {We characterize compact sets $X$ in the Riemann sphere $\mathbb \{S\}$ not separating $\mathbb \{S\}$ for which the algebra $A(X)$ of all functions continuous on $\mathbb \{S\}$ and holomorphic on $\mathbb \{S\}\setminus X$, restricted to the set $X$, is pervasive on $X$.},
author = {Čerych, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); pervasive algebras; the algebra $A(X)$ of all functions continuous on $\mathbb \{S\}$ and holomorphic on $\mathbb \{S\}\setminus X$; pervasive algebras},
language = {eng},
number = {3},
pages = {491-494},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Pervasive algebras on planar compacts},
url = {http://eudml.org/doc/248393},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Čerych, Jan
TI - Pervasive algebras on planar compacts
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 491
EP - 494
AB - We characterize compact sets $X$ in the Riemann sphere $\mathbb {S}$ not separating $\mathbb {S}$ for which the algebra $A(X)$ of all functions continuous on $\mathbb {S}$ and holomorphic on $\mathbb {S}\setminus X$, restricted to the set $X$, is pervasive on $X$.
LA - eng
KW - compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); pervasive algebras; the algebra $A(X)$ of all functions continuous on $\mathbb {S}$ and holomorphic on $\mathbb {S}\setminus X$; pervasive algebras
UR - http://eudml.org/doc/248393
ER -