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

top
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

top

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

top
  1. Baran M., Separation properties, Indian J. Pure Appl. Math. 23 (1992), 13-21. (1992) Zbl0876.54009MR1166899
  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. 
  5. Harvey J.M., T 0 -separation in topological categories, Quastiones Math. 2 (1977), 177-190. (1977) Zbl0384.18002MR0486050
  6. Herrlich H., Topological functors, Gen. Top. Appl. 4 (1974), 125-142. (1974) Zbl0288.54003MR0343226
  7. Hoffmann R.-E., ( E , M ) -Universally Topological Functors, Habilitationsschrift, Universität Düsseldorf, 1974. 
  8. Hosseini N., The Geometric Realization Functors and Preservation of Finite Limits, Dissertation, University of Miami, 1986. 
  9. Hušek M., Pumplün D., Disconnectedness, Quaestiones Math. 13 (1990), 449-459. (1990) MR1084754
  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) MR1123910

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.