| Title:
|
Modular, distributive and simple intervals of the lattice of topologies (English) |
| Author:
|
Rosický, Jiří |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
11 |
| Issue:
|
2 |
| Year:
|
1975 |
| Pages:
|
105-114 |
| . |
| Category:
|
math |
| . |
| MSC:
|
06C05 |
| MSC:
|
06D05 |
| MSC:
|
54A10 |
| idZBL:
|
Zbl 0347.54006 |
| idMR:
|
MR0410621 |
| . |
| Date available:
|
2008-06-05T19:56:21Z |
| Last updated:
|
2012-05-09 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104847 |
| . |
| Reference:
|
[1] C. E. Aull, W. J. Thron: Separation axioms between $T_0$ and $T_1$.Nederl. akad. Wetensch. Proc. Ser. A 65 = Indag. Math. 24 (1962), 26-37. MR 0138082 |
| Reference:
|
[2] R. W. Bagley, D. Ellis: On the topolattice and permutation group of an infinite set.Math.. Japon. 3 (1954), 63-70. MR 0069480 |
| Reference:
|
[3] N. Bourbaki: Topologie générale.Paris. Zbl 1107.54001 |
| Reference:
|
[4] A. M. Carstens: The lattice of pretopologies on an arbitrary set S.Pac Jour. Math. 29 (1969),, 67-71. Zbl 0179.51001, MR 0243476 |
| Reference:
|
[5] E. Čech: Topological spaces.Prague 1966. MR 0211373 |
| Reference:
|
[6] Ph. Dwinger: On the lattice of the closure operators of a complete lattice.Nieuw Arch. Wisk. (4), IV (1956), 112-117. Zbl 0074.02204, MR 0081882 |
| Reference:
|
[7] A. G. Eľkin: Ultrafiltry i nerazložimyje prostranstva.Vest. Mosk. Univ., Ser. I, 24, No 5 (1969), 51-56. MR 0263004 |
| Reference:
|
[8] O. Fröhlich: Das Halbordnungssystem der topologischen Räume auf einer Menge.Math. Ann. 156 (1964), 79-95. MR 0166750 |
| Reference:
|
[9] J. Hartmanis: On the lattice of topologies.Can. Jour. Math. 10 (1958), 547-553. Zbl 0087.37403, MR 0098358 |
| Reference:
|
[10] E. Hewitt: A problem of set-theoretic topology.Duke math. J. 10 (1943), 309-333. Zbl 0060.39407, MR 0008692 |
| Reference:
|
[11] H. J. Kowalsky: Topological spaces.New York, London 1965. |
| Reference:
|
[12] R. E. Larson: Minimal $T_0$-spaces and minimal $T_D$-spaces.Pac. Jour. Math. 31 (1969), 451-458. MR 0251688 |
| Reference:
|
[13] R. E. Larson, S. J. Zimmerman: The lattice of topologies: A survey.to appear. |
| Reference:
|
[14] J. Rosický: Topologies compatible with ordering.Publ. Fac. Sci. Univ. Brno, 1971, 9-23. MR 0326682 |
| Reference:
|
[15] J. Rosický: Relative Komplemente im Verband der $T_1$-Topologien.Publ. Fac. Sci. Univ. Brno, 518 (1970), 445-460. MR 0289382 |
| Reference:
|
[16] J. Rosický: Embeddings of lattices in the lattice of topologies.Arch. Math. Brno, to appear. MR 0372803 |
| Reference:
|
[17] M. Sekanina: Sistěmy topologij na dannom množestve.Czech. Math. Jour. T 15 (90), 1965, 9-29. |
| Reference:
|
[18] A. K. Steiner: The lattice of topologies: Structure and complementation.Trans. Amer. Math. Soc. 122 (1966), 379-398. Zbl 0139.15905, MR 0190893 |
| Reference:
|
[19] G. Szasz: Einführung in die Verbandstheorie.Budapest 1962. Zbl 0101.26901, MR 0138567 |
| Reference:
|
[20] R. Valent, R. E. Larson: Basic Intervals in the Lattice of Topologies.Duke Math. J. 39 (1972), 401-411. Zbl 0312.06014, MR 0305322 |
| . |
