Geodesic
The category of compactifications and its coreflections
Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 3, pp. 365-378.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We define ``the category of compactifications'', which is denoted {\bf{CM}}, and consider its family of coreflections, denoted {\bf{corCM}}. We show that {\bf{corCM}} is a complete lattice with bottom the identity and top an interpretation of the Čech--Stone $\beta$. A $c \in${\bf{corCM}} implies the assignment to each locally compact, noncompact $Y$ a compactification minimum for membership in the ``object-range'' of $c$. We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms in {\bf{corCM}} (thus {\bf{corCM}} is not a set), show that any $c \in${\bf{corCM}} not the identity is above an atom, and that $\beta$ is not the supremum of atoms.
DOI : 10.14712/1213-7243.2022.024
Classification : 06B23, 18A40, 54B30, 54C10, 54D35
Keywords: compactification; coreflection; atom in a lattice 
@article{10_14712_1213_7243_2022_024,
     author = {Hager, Anthony W. and Wynne, Brian},
     title = {The category of compactifications and its coreflections},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {365--378},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {2022},
     doi = {10.14712/1213-7243.2022.024},
     mrnumber = {4542795},
     zbl = {07655806},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.024/}
}
TY  - JOUR
AU  - Hager, Anthony W.
AU  - Wynne, Brian
TI  - The category of compactifications and its coreflections
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2022
SP  - 365
EP  - 378
VL  - 63
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.024/
DO  - 10.14712/1213-7243.2022.024
LA  - en
ID  - 10_14712_1213_7243_2022_024
ER  - 
%0 Journal Article
%A Hager, Anthony W.
%A Wynne, Brian
%T The category of compactifications and its coreflections
%J Commentationes Mathematicae Universitatis Carolinae
%D 2022
%P 365-378
%V 63
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.024/
%R 10.14712/1213-7243.2022.024
%G en
%F 10_14712_1213_7243_2022_024
Hager, Anthony W.; Wynne, Brian. The category of compactifications and its coreflections. Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 3, pp. 365-378. doi : 10.14712/1213-7243.2022.024. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.024/

Cité par Sources :