| Title:
|
The notion of closedness in topological categories (English) |
| Author:
|
Baran, Mehmet |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
383-395 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
topological category |
| Keyword:
|
separation properties |
| Keyword:
|
(strongly) closed objects |
| MSC:
|
18B99 |
| MSC:
|
18D15 |
| MSC:
|
54A05 |
| MSC:
|
54A20 |
| MSC:
|
54B30 |
| MSC:
|
54D10 |
| idZBL:
|
Zbl 0780.18003 |
| idMR:
|
MR1241748 |
| Note:
|
XXX špatné pořadí stránek () |
| . |
| Date available:
|
2009-01-08T18:04:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118592 |
| . |
| Reference:
|
[1] Baran M.: Separation properties.Indian J. Pure Appl. Math. 23 (1992), 13-21. Zbl 0876.54009, MR 1166899 |
| Reference:
|
[2] Baran M.: Stacks and filters.Turkish J. of Math.-Doğa 16 (1992), 94-107. Zbl 0841.54004, MR 1180841 |
| Reference:
|
[3] Baran M., Mielke M.V.: Generalized Separation Properties in Topological Categories.in preparation. |
| Reference:
|
[4] Brümmer G.C.L.: A Categorical Study of Initiality in Uniform Topology.Thesis, University of Cape Town, 1971. |
| Reference:
|
[5] Harvey J.M.: $T_0$-separation in topological categories.Quastiones Math. 2 (1977), 177-190. Zbl 0384.18002, MR 0486050 |
| Reference:
|
[6] Herrlich H.: Topological functors.Gen. Top. Appl. 4 (1974), 125-142. Zbl 0288.54003, MR 0343226 |
| Reference:
|
[7] Hoffmann R.-E.: $(E,M)$-Universally Topological Functors.Habilitationsschrift, Universität Düsseldorf, 1974. |
| Reference:
|
[8] Hosseini N.: The Geometric Realization Functors and Preservation of Finite Limits.Dissertation, University of Miami, 1986. |
| Reference:
|
[9] Hušek M., Pumplün D.: Disconnectedness.Quaestiones Math. 13 (1990), 449-459. MR 1084754 |
| Reference:
|
[10] Marny Th.: Rechts-Bikategoriestrukturen in topologischen Kategorien.Dissertation, Freie Universität Berlin, 1973. |
| Reference:
|
[11] Mielke M.V.: Convenient categories for internal singular algebraic topology.Illinois Journal of Math., vol. 27, no. 3, 1983. Zbl 0496.55006, MR 0698313 |
| Reference:
|
[12] Mielke M.V.: Geometric topological completions with universal final lifts.Top. and Appl. 9 (1985), 277-293. Zbl 0581.18004, MR 0794490 |
| Reference:
|
[13] Munkres J.R.: Topology: A First Course.Prentice Hall Inc., New Jersey, 1975. Zbl 0306.54001, MR 0464128 |
| Reference:
|
[14] Nel L.D.: Initially structured categories and cartesian closedness.Can. Journal of Math. XXVII (1975), 1361-1377. Zbl 0294.18002, MR 0393183 |
| Reference:
|
[15] Schwarz F.: Connections Between Convergence and Nearness.Lecture Notes in Math. 719, Springer-Verlag, 1978, pp. 345-354. Zbl 0409.54002, MR 0544658 |
| Reference:
|
[16] Weck-Schwarz S.: $T_0$-objects and separated objects in topological categories.Quastiones Math. 14 (1991), 315-325. MR 1123910 |
| . |
