Generalized intervals and topology

Robert H. Redfield

Czechoslovak Mathematical Journal (1976)

  • Volume: 26, Issue: 4, page 527-540
  • ISSN: 0011-4642

How to cite

top

Redfield, Robert H.. "Generalized intervals and topology." Czechoslovak Mathematical Journal 26.4 (1976): 527-540. <http://eudml.org/doc/12964>.

@article{Redfield1976,
author = {Redfield, Robert H.},
journal = {Czechoslovak Mathematical Journal},
language = {eng},
number = {4},
pages = {527-540},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized intervals and topology},
url = {http://eudml.org/doc/12964},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Redfield, Robert H.
TI - Generalized intervals and topology
JO - Czechoslovak Mathematical Journal
PY - 1976
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 4
SP - 527
EP - 540
LA - eng
UR - http://eudml.org/doc/12964
ER -

References

top
  1. R. A. Alo O. Frink, 10.4153/CJM-1966-101-2, Canadian J. Math. 18 (1966), pp. 1004-1014. (1966) Zbl0148.01401MR0209195DOI10.4153/CJM-1966-101-2
  2. G. Birkhoff, Lattice Theory, (second edition). Amer. Math. Soc. Colloquium Pub. 25, Providence, R.I., 1948. (1948) Zbl0033.10103MR0029876
  3. G. Birkhoff, A new interval topology for dually directed sets, Revista Mat. y Fis. Teorica Tucuman 14 (1962), pp. 325-331. (1962) Zbl0135.22702MR0166120
  4. G. Birkhoff, Lattice Theory, (third revised edition). Amer. Math. Soc. Colloquium Pub. 25, Providence, R.I., 1967. (1967) Zbl0153.02501MR0227053
  5. G. Birkhoff O. Frink, 10.1090/S0002-9947-1948-0027263-2, Trans. Amer. Math. Soc. 64 (1948), pp. 299-316. (1948) Zbl0032.00504MR0027263DOI10.1090/S0002-9947-1948-0027263-2
  6. N. Bourbaki, General Topology, Part 1, Addison-Wesley Pub. Co., Don Mills, Ont., 1966 (translated from the French, Topologie Générale, Hermann, Paris). (1966) Zbl0301.54001
  7. P. Conrad, Lex-subgroups of lattice-ordered groups, Czech. Math. J. 18 (1968), pp. 86-103. (1968) Zbl0155.05902MR0225697
  8. W. Doyle, An arithmetical theorem for partially ordered sets, Bull. Amer. Math. Soc. 56 (1950), p. 366. (1950) 
  9. O. Frink, 10.1090/S0002-9947-1942-0006496-X, Trans. Amer. Math. Soc. 51 (1942), pp. 569-582. (1942) Zbl0061.39305MR0006496DOI10.1090/S0002-9947-1942-0006496-X
  10. O. Frink, 10.2307/2306387, Amer. Math. Monthly 61 (1954), pp. 223 - 234. (1954) Zbl0055.25901MR0061575DOI10.2307/2306387
  11. M. Guillaume, Sur les topologies définies à partir d'une relation d'ordre, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8° 29 (1956), no. 6. (1956) Zbl0073.27001MR0102484
  12. C. Holland, The interval topology of a certain l -group, Czech. Math. J. 15 (1965), pp. 311-314. (1965) Zbl0137.25702MR0177044
  13. J. Jakubík, The interval topology of an l -group, Coll. Math. 11 (1963), pp. 65-72. (1963) Zbl0122.28002MR0160831
  14. J. L. Kelley, General Topology, D. van Nostrand Co., Inc., Princeton, 1955. (1955) Zbl0066.16604MR0070144
  15. J. D. Lawson, Intrinsic lattice and semilattice topologies, Proceedings of the Conference on Lattice Theory (1973), University of Houston, to аррeаr. (1973) Zbl0293.06011MR0401576
  16. R. J. Loy J. B. Miller, Tight Riesz Groups, J. Australian Math. Soc. 13 (1972), pp. IIA-IAO. (1972) Zbl0243.06011MR0297669
  17. H. Mayer M. Novotný, On some topologies on products of ordered sets, Arch. Math. (Brno) 1 (1965), pp. 251-257. (1965) Zbl0178.34002MR0195071
  18. T. Naito, 10.2748/tmj/1178244439, Tohoku Math. J. (2) 12 (1960), pp. 235-262. (1960) Zbl0094.01801MR0121319DOI10.2748/tmj/1178244439
  19. R. H. Redfield, 10.1090/S0002-9947-1974-0327607-3, Trans. Amer. Math. Soc. 187 (1974), pp. 103-125. (1974) Zbl0302.06028MR0327607DOI10.1090/S0002-9947-1974-0327607-3
  20. B. С. Rennie, Lattices, Proc. Lon. Math. Soc. 52 (1951), pp. 386-400. (1951) Zbl0044.37901MR0690634
  21. B. C. Rennie, Lattices, Foister & Jagg, Cambridge, 1952. (1952) Zbl0042.41004
  22. F. Šik, Zur Theorie der halbgeordnete Gruppen, Czech. Math. J. 6 (1956), pp. 1 - 25. (1956) Zbl0075.01504MR0081907
  23. A. J. Ward, On relations between certain intrinsic topologies in partially ordered sets, Proc. Cambridge Phil. Soc. 51 (1955), pp. 254-261. (1955) Zbl0066.02101MR0070995

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.