A generating family for the Freudenthal compactification of a class of rimcompact spaces

Jesús M. Domínguez. "A generating family for the Freudenthal compactification of a class of rimcompact spaces." Fundamenta Mathematicae 178.3 (2003): 203-215. <http://eudml.org/doc/282914>.

@article{JesúsM2003,
abstract = {For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of $F(X)/C_\{K\}(X)$ and the lattice of all compactifications of X with zero-dimensional remainder, the finite-dimensional subalgebras corresponding to the compactifications with finite remainder.},
author = {Jesús M. Domínguez},
journal = {Fundamenta Mathematicae},
keywords = {compactification; rimcompact; ring of continuous functions; function algebra; Boolean ring; maximal ideal; idempotent; zero-dimensional},
language = {eng},
number = {3},
pages = {203-215},
title = {A generating family for the Freudenthal compactification of a class of rimcompact spaces},
url = {http://eudml.org/doc/282914},
volume = {178},
year = {2003},
}

TY - JOUR
AU - Jesús M. Domínguez
TI - A generating family for the Freudenthal compactification of a class of rimcompact spaces
JO - Fundamenta Mathematicae
PY - 2003
VL - 178
IS - 3
SP - 203
EP - 215
AB - For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of $F(X)/C_{K}(X)$ and the lattice of all compactifications of X with zero-dimensional remainder, the finite-dimensional subalgebras corresponding to the compactifications with finite remainder.
LA - eng
KW - compactification; rimcompact; ring of continuous functions; function algebra; Boolean ring; maximal ideal; idempotent; zero-dimensional
UR - http://eudml.org/doc/282914
ER -