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

A. Caterino; G. Dimov; M. C. Vipera

Bollettino dell'Unione Matematica Italiana (2002)

- Volume: 5-B, Issue: 3, page 839-858
- ISSN: 0392-4041

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topCaterino, 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 -

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