$A$-compactifications and $A$-weight of Alexandroff spaces

Caterino, A., Dimov, G., and Vipera, M. C.. "$A$-compactifications and $A$-weight of Alexandroff spaces." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 839-858. <http://eudml.org/doc/195238>.

@article{Caterino2002,
abstract = {The paper is devoted to the study of the ordered set $A \mathcal\{K\}(X, \alpha)$ of all, up to equivalence, $A$-compactifications of an Alexandroff space $(X, \alpha)$. The notion of $A$-weight (denoted by $aw(X, \alpha)$) of an Alexandroff space $(X, \alpha)$ is introduced and investigated. Using results in ([7]) and ([5]), lattice properties of $A \mathcal\{K\}(X, \alpha)$ and $A \mathcal\{K_\{\alpha w\}\}(X, \alpha)$ are studied, where $A \mathcal\{K_\{\alpha w\}\}(X, \alpha)$ is the set of all, up to equivalence, $A$-compactifications $Y$ of $(X, \alpha)$ for which $w(Y)= a w(X, \alpha)$. A characterization of the families of bounded functions generating an $A$-compactification of $(X, \alpha)$ is obtained. The notion of $A$-determining family of functions, analogous to the one of determining family given in ([3]), is introduced and relations with the original notion are investigated. A characterization of the families of functions which $A$-determine a given $A$-compactification is found. The cardinal invariant $a\delta(Y, t)$, corresponding to the cardinal invariant $\delta(Y, t)$ defined in ([3]), is introduced and studied.},
author = {Caterino, A., Dimov, G., Vipera, M. C.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {839-858},
publisher = {Unione Matematica Italiana},
title = {$A$-compactifications and $A$-weight of Alexandroff spaces},
url = {http://eudml.org/doc/195238},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Caterino, A.
AU - Dimov, G.
AU - Vipera, M. C.
TI - $A$-compactifications and $A$-weight of Alexandroff spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 839
EP - 858
AB - The paper is devoted to the study of the ordered set $A \mathcal{K}(X, \alpha)$ of all, up to equivalence, $A$-compactifications of an Alexandroff space $(X, \alpha)$. The notion of $A$-weight (denoted by $aw(X, \alpha)$) of an Alexandroff space $(X, \alpha)$ is introduced and investigated. Using results in ([7]) and ([5]), lattice properties of $A \mathcal{K}(X, \alpha)$ and $A \mathcal{K_{\alpha w}}(X, \alpha)$ are studied, where $A \mathcal{K_{\alpha w}}(X, \alpha)$ is the set of all, up to equivalence, $A$-compactifications $Y$ of $(X, \alpha)$ for which $w(Y)= a w(X, \alpha)$. A characterization of the families of bounded functions generating an $A$-compactification of $(X, \alpha)$ is obtained. The notion of $A$-determining family of functions, analogous to the one of determining family given in ([3]), is introduced and relations with the original notion are investigated. A characterization of the families of functions which $A$-determine a given $A$-compactification is found. The cardinal invariant $a\delta(Y, t)$, corresponding to the cardinal invariant $\delta(Y, t)$ defined in ([3]), is introduced and studied.
LA - eng
UR - http://eudml.org/doc/195238
ER -