𝒯 0 - and 𝒯 1 -reflections

Maria Manuel Clementino

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 493-504
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Clementino, Maria Manuel. "$\mathcal {T}_0$- and $\mathcal {T}_1$-reflections." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 493-504. <http://eudml.org/doc/21877>.

@article{Clementino1992,
abstract = {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.},
author = {Clementino, Maria Manuel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {factorization system; closure operator; separation axioms; prereflection; reflection; subobject; closure; point; prereflections; iterations; reflectors},
language = {eng},
number = {3},
pages = {493-504},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\mathcal \{T\}_0$- and $\mathcal \{T\}_1$-reflections},
url = {http://eudml.org/doc/21877},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Clementino, Maria Manuel
TI - $\mathcal {T}_0$- and $\mathcal {T}_1$-reflections
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 493
EP - 504
AB - 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.
LA - eng
KW - factorization system; closure operator; separation axioms; prereflection; reflection; subobject; closure; point; prereflections; iterations; reflectors
UR - http://eudml.org/doc/21877
ER -

References

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  1. Arhangel'skiĭ, Wiegandt R., Connectednesses and disconnectednesses in topology, Topology Appl. 5 (1975), 9-33. (1975) MR0367920
  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). MR0211373
  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. (1987) Zbl0634.54008MR0911687
  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. MR1047909
  8. Giuli E., Bases of topological epireflections, Topology Appl. 11 (1980), 265-273. (1980) MR0585271
  9. Harvey J.M., T 0 -separation in topological categories, Quaest. Mathematicae 2 (1977), 177-190. (1977) Zbl0384.18002MR0486050
  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. (1990) MR1084754
  12. Hušek M., Pumplün D., Note on separation in categories, preprint, 1991. MR1276007
  13. MacLane S., Categories for the working mathematician, Springer-Verlag, Berlin-Heidelberg- New York, 1971. Zbl0705.18001MR0354798
  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. (1979) Zbl0415.54007MR0527843
  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. MR0544654
  17. Salicrup G., Vasquez R., Connection and disconnection, Lecture Notes in Math. 719 (SpringerVerlag, Berlin-Heidelberg-New York, 1979), 326-344. MR0544657
  18. Tholen W., Factorizations, localizations and the orthogonal subcategory problem, Math. Nachr. 114 (1983), 63-85. (1983) Zbl0553.18003MR0745048
  19. Tholen W., Factorizations, fibres and connectedness, Categorical Topology, Proc. Conference Toledo, Ohio, 1983 (Heldermann Verlag, Berlin, 1984), 549-566. Zbl0547.18001MR0785035
  20. Tholen W., Prereflections and reflections, Comm. Algebra 14 (1986), 717-740. (1986) Zbl0587.18002MR0830816
  21. Tiller J.A., Component subcategories, Quaest. Mathematicae 4 (1980), 19-40. (1980) Zbl0431.18001MR0573837
  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. (1991) MR1123910

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