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

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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

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  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

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