The notion of closedness in topological categories

Mehmet Baran

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 383-395
  • ISSN: 0010-2628

Abstract

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In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated in an arbitrary topological category and a characterization of each of these notions is given for some known topological categories.

How to cite

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Baran, Mehmet. "The notion of closedness in topological categories." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 383-395. <http://eudml.org/doc/21948>.

@article{Baran1993,
abstract = {In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated in an arbitrary topological category and a characterization of each of these notions is given for some known topological categories.},
author = {Baran, Mehmet},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological category; separation properties; (strongly) closed objects; closed objects; topological category; generalized separation properties},
language = {eng},
number = {2},
pages = {383-395},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The notion of closedness in topological categories},
url = {http://eudml.org/doc/21948},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Baran, Mehmet
TI - The notion of closedness in topological categories
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 383
EP - 395
AB - In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated in an arbitrary topological category and a characterization of each of these notions is given for some known topological categories.
LA - eng
KW - topological category; separation properties; (strongly) closed objects; closed objects; topological category; generalized separation properties
UR - http://eudml.org/doc/21948
ER -

References

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  2. Baran M., Stacks and filters, Turkish J. of Math.-Doğa 16 (1992), 94-107. (1992) Zbl0841.54004MR1180841
  3. Baran M., Mielke M.V., Generalized Separation Properties in Topological Categories, in preparation. 
  4. Brümmer G.C.L., A Categorical Study of Initiality in Uniform Topology, Thesis, University of Cape Town, 1971. 
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  7. Hoffmann R.-E., ( E , M ) -Universally Topological Functors, Habilitationsschrift, Universität Düsseldorf, 1974. 
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  10. Marny Th., Rechts-Bikategoriestrukturen in topologischen Kategorien, Dissertation, Freie Universität Berlin, 1973. 
  11. Mielke M.V., Convenient categories for internal singular algebraic topology, Illinois Journal of Math., vol. 27, no. 3, 1983. Zbl0496.55006MR0698313
  12. Mielke M.V., Geometric topological completions with universal final lifts, Top. and Appl. 9 (1985), 277-293. (1985) Zbl0581.18004MR0794490
  13. Munkres J.R., Topology: A First Course, Prentice Hall Inc., New Jersey, 1975. Zbl0306.54001MR0464128
  14. Nel L.D., Initially structured categories and cartesian closedness, Can. Journal of Math. XXVII (1975), 1361-1377. (1975) Zbl0294.18002MR0393183
  15. Schwarz F., Connections Between Convergence and Nearness, Lecture Notes in Math. 719, Springer-Verlag, 1978, pp. 345-354. Zbl0409.54002MR0544658
  16. Weck-Schwarz S., T 0 -objects and separated objects in topological categories, Quastiones Math. 14 (1991), 315-325. (1991) Zbl0756.54011MR1123910

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