Modular, distributive and simple intervals of the lattice of topologies

Jiří Rosický

Archivum Mathematicum (1975)

  • Volume: 011, Issue: 2, page 105-114
  • ISSN: 0044-8753

How to cite

top

Rosický, Jiří. "Modular, distributive and simple intervals of the lattice of topologies." Archivum Mathematicum 011.2 (1975): 105-114. <http://eudml.org/doc/15990>.

@article{Rosický1975,
author = {Rosický, Jiří},
journal = {Archivum Mathematicum},
language = {eng},
number = {2},
pages = {105-114},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Modular, distributive and simple intervals of the lattice of topologies},
url = {http://eudml.org/doc/15990},
volume = {011},
year = {1975},
}

TY - JOUR
AU - Rosický, Jiří
TI - Modular, distributive and simple intervals of the lattice of topologies
JO - Archivum Mathematicum
PY - 1975
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 011
IS - 2
SP - 105
EP - 114
LA - eng
UR - http://eudml.org/doc/15990
ER -

References

top
  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. (1962) MR0138082
  2. R. W. Bagley, D. Ellis, On the topolattice and permutation group of an infinite set, Math.. Japon. 3 (1954), 63-70. (1954) MR0069480
  3. N. Bourbaki, Topologie générale, Paris. Zbl1107.54001
  4. A. M. Carstens, The lattice of pretopologies on an arbitrary set S, Pac Jour. Math. 29 (1969),, 67-71. (1969) Zbl0179.51001MR0243476
  5. E. Čech, Topological spaces, Prague 1966. (1966) MR0211373
  6. Ph. Dwinger, On the lattice of the closure operators of a complete lattice, Nieuw Arch. Wisk. (4), IV (1956), 112-117. (1956) Zbl0074.02204MR0081882
  7. A. G. Eľkin, Ultrafiltry i nerazložimyje prostranstva, Vest. Mosk. Univ., Ser. I, 24, No 5 (1969), 51-56. (1969) MR0263004
  8. O. Fröhlich, Das Halbordnungssystem der topologischen Räume auf einer Menge, Math. Ann. 156 (1964), 79-95. (1964) MR0166750
  9. J. Hartmanis, On the lattice of topologies, Can. Jour. Math. 10 (1958), 547-553. (1958) Zbl0087.37403MR0098358
  10. E. Hewitt, A problem of set-theoretic topology, Duke math. J. 10 (1943), 309-333. (1943) Zbl0060.39407MR0008692
  11. H. J. Kowalsky, Topological spaces, New York, London 1965. (1965) 
  12. R. E. Larson, Minimal T 0 -spaces and minimal T D -spaces, Pac. Jour. Math. 31 (1969), 451-458. (1969) MR0251688
  13. R. E. Larson, S. J. Zimmerman, The lattice of topologies: A survey, to appear. 
  14. J. Rosický, Topologies compatible with ordering, Publ. Fac. Sci. Univ. Brno, 1971, 9-23. (1971) MR0326682
  15. J. Rosický, Relative Komplemente im Verband der T 1 -Topologien, Publ. Fac. Sci. Univ. Brno, 518 (1970), 445-460. (1970) MR0289382
  16. J. Rosický, Embeddings of lattices in the lattice of topologies, Arch. Math. Brno, to appear. MR0372803
  17. M. Sekanina, Sistěmy topologij na dannom množestve, Czech. Math. Jour. T 15 (90), 1965, 9-29. (1965) 
  18. A. K. Steiner, The lattice of topologies: Structure and complementation, Trans. Amer. Math. Soc. 122 (1966), 379-398. (1966) Zbl0139.15905MR0190893
  19. G. Szasz, Einführung in die Verbandstheorie, Budapest 1962. (1962) Zbl0101.26901MR0138567
  20. R. Valent, R. E. Larson, Basic Intervals in the Lattice of Topologies, Duke Math. J. 39 (1972), 401-411. (1972) Zbl0312.06014MR0305322

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.