Pacific Journal of Mathematics

Complementation in the lattice of regular topologies.

M. Jeanette Huebener

Article information

Source
Pacific J. Math., Volume 43, Number 1 (1972), 139-149.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102959649

Mathematical Reviews number (MathSciNet)
MR0315644

Zentralblatt MATH identifier
0244.54002

Subjects
Primary: 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

Citation

Huebener, M. Jeanette. Complementation in the lattice of regular topologies. Pacific J. Math. 43 (1972), no. 1, 139--149. https://projecteuclid.org/euclid.pjm/1102959649


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References

  • [1] B. A. Anderson, A class of topologies with T complements, Notices Amer. Math. Soc, 16 (1969), 69T-G141, 989.
  • [2] B. A. Anderson and D. G. Stewart, T complements of T topologies, Proc. Amer. Math. Soc, 23 (1970), 77-81.
  • [3] R. W. Bagley, On the characterization of the lattice of topologies, J. London Math. Soc, 30 (1955), 247-249.
  • [4] N. Bourbaki, Topologie Generale, Hermann, Paris, 1961.
  • [5] Oc Frohlich, Das Halbordnunssystemder topologischen Raume auf einerMange, Math. Ann., 156 (1964), 79-95.
  • [6] H. Gaifman, The lattice of all topologies, Canad. J. Math., 18 (1966), 83-85.
  • [7] J. Hartmanis, On the lattice of topologies, Canad. J. Math., 10 (1958), 547-553.
  • [8] M. J. Norris, A note on regular and completely regular topological spaces, Proc Amer. Math. Soc, 1 (1950), 754-755.
  • [9] W. J. Pervin, Foundations of General Topology, Academic Press, New York, 1964.
  • [10] A. K. Steiner, The lattice of topologies: structureand complementation, Trans. Amer. Math. Soc, 122 (1966), 379-398.
  • [11] A. K. Steiner, Complementation in the lattice of Ti topologies, Proc Amer. Math. Soc, 17 (1967), 884-886.
  • [12] A. K. Steiner and E. F. Steiner, Topologies with T\ complements, Fund. Math., 61 (1967), 23-28.
  • [13] A. K. Steiner and E. F. Steiner, A Ti complement for the reals, Proc. Amer. Math. Soc, 19 (1968) 177-179.
  • [14] J. P. Thomas, Associated regular spaces, Canad. J. Math., 20 (1968), 1087-1092.
  • [15] W. J. Thron, Topological Structures,Holt Rinehart Winston, New York, 1966.
  • [16] A. C. M. van Rooij, The lattice of all topologies is complemented, Canad. J. Math., 20 (1968), 805-807.