Geodesic
$\Cal T_0$- and $\Cal T_1$-reflections
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 493-504 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms $T_0$ and $T_1$. Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.
In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms $T_0$ and $T_1$. Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.
Classification : 18A32, 18A40, 18B30, 54A05, 54D10
Keywords: factorization system; closure operator; separation axioms; prereflection; reflection 
@article{CMUC_1992_33_3_a11,
     author = {Clementino, Maria Manuel},
     title = {$\Cal T_0$- and $\Cal T_1$-reflections},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {493--504},
     year = {1992},
     volume = {33},
     number = {3},
     mrnumber = {1209291},
     zbl = {0842.18002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a11/}
}
TY  - JOUR
AU  - Clementino, Maria Manuel
TI  - $\Cal T_0$- and $\Cal T_1$-reflections
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1992
SP  - 493
EP  - 504
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a11/
LA  - en
ID  - CMUC_1992_33_3_a11
ER  - 
%0 Journal Article
%A Clementino, Maria Manuel
%T $\Cal T_0$- and $\Cal T_1$-reflections
%J Commentationes Mathematicae Universitatis Carolinae
%D 1992
%P 493-504
%V 33
%N 3
%U http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a11/
%G en
%F CMUC_1992_33_3_a11
Clementino, Maria Manuel. $\Cal T_0$- and $\Cal T_1$-reflections. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 493-504. http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a11/

[1] Arhangel'skiĭ, Wiegandt R.: Connectednesses and disconnectednesses in topology. Topology Appl. 5 (1975), 9-33. | MR

[2] Börger R.: Kategorielle Beschreibungen von Zusammenhangsbegriffen. Ph.D. Thesis, Fernuniversität Hagen, 1981.

[3] Brümmer G.C.L.: A categorical study of initiality in uniform topology. Ph.D. Thesis, University of Cape Town, 1971.

[4] Čech E.: Topological spaces. revised by Z. Frolík and M. Katětov (Academia, Praha, 1966). | MR

[5] Clementino M.M.: Ph.D. Thesis, Universidade de Coimbra (in preparation).

[6] Dikranjan D., Giuli E.: Closure operators I. Topology Appl. 27 (1987), 129-143. | MR | Zbl

[7] Dikranjan D., Giuli E., Tholen W.: Closure operators II, Categorical topology and its relations to analysis, algebra and combinatorics. Proc. Int. Conf. Prague, 1988 (World Scientific, Singapore-New Jersey-London-Hong Kong), 297-335. | MR

[8] Giuli E.: Bases of topological epireflections. Topology Appl. 11 (1980), 265-273. | MR

[9] Harvey J.M.: $T_0$-separation in topological categories. Quaest. Mathematicae 2 (1977), 177-190. | MR | Zbl

[10] Hoffmann R.-E.: $(E,M)$-universally topological functors. Habilitationsschrift, Universität Düsseldorf, 1974.

[11] Hušek M., Pumplün D.: Disconnectedness. Quaest. Mathematicae 13 (1990), 449-459. | MR

[12] Hušek M., Pumplün D.: Note on separation in categories. preprint, 1991. | MR

[13] MacLane S.: Categories for the working mathematician. Springer-Verlag, Berlin-Heidelberg- New York, 1971. | MR | Zbl

[14] Mantovani S.: Connessione e totale reflessività. Ph.D. Thesis, Università di Milano, 1988.

[15] Marny T.: On epireflective subcategories of topological categories. Gen. Top. Appl. 10 (1979), 175-181. | MR | Zbl

[16] Preuß G.: Connection properties in topological categories and related topics. Lecture Notes in Math. 719 (Springer-Verlag, Berlin-Heidelberg-New York, 1979), 293-305. | MR

[17] Salicrup G., Vasquez R.: Connection and disconnection. Lecture Notes in Math. 719 (SpringerVerlag, Berlin-Heidelberg-New York, 1979), 326-344. | MR

[18] Tholen W.: Factorizations, localizations and the orthogonal subcategory problem. Math. Nachr. 114 (1983), 63-85. | MR | Zbl

[19] Tholen W.: Factorizations, fibres and connectedness. Categorical Topology, Proc. Conference Toledo, Ohio, 1983 (Heldermann Verlag, Berlin, 1984), 549-566. | MR | Zbl

[20] Tholen W.: Prereflections and reflections. Comm. Algebra 14 (1986), 717-740. | MR | Zbl

[21] Tiller J.A.: Component subcategories. Quaest. Mathematicae 4 (1980), 19-40. | MR | Zbl

[22] Weck-Schwarz S.: Cartesish abgeschlossene monotopologische Hüllen und die Rolle der $T_0$-Reflexionen. Ph.D. Thesis, Universität Hannover, 1988.

[23] Weck-Schwarz S.: $T_0$-objects and separated objects in topological categories. Quaest. Mathematicae 14 (1991), 315-325. | MR