| Title:
|
Generalized intervals and topology (English) |
| Author:
|
Redfield, R. H. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
26 |
| Issue:
|
4 |
| Year:
|
1976 |
| Pages:
|
527-540 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
06A45 |
| idZBL:
|
Zbl 0362.06018 |
| idMR:
|
MR0439707 |
| DOI:
|
10.21136/CMJ.1976.101426 |
| . |
| Date available:
|
2008-06-09T14:20:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101426 |
| . |
| Reference:
|
[1] R. A. Alo O. Frink: Topologies of lattice products.Canadian J. Math. 18 (1966), pp. 1004-1014. MR 0209195, 10.4153/CJM-1966-101-2 |
| Reference:
|
[2] G. Birkhoff: Lattice Theory.(second edition). Amer. Math. Soc. Colloquium Pub. 25, Providence, R.I., 1948. Zbl 0033.10103, MR 0029876 |
| Reference:
|
[3] G. Birkhoff: A new interval topology for dually directed sets.Revista Mat. y Fis. Teorica Tucuman 14 (1962), pp. 325-331. Zbl 0135.22702, MR 0166120 |
| Reference:
|
[4] G. Birkhoff: Lattice Theory.(third revised edition). Amer. Math. Soc. Colloquium Pub. 25, Providence, R.I., 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[5] G. Birkhoff O. Frink: Representations of lattices by sets.Trans. Amer. Math. Soc. 64 (1948), pp. 299-316. MR 0027263, 10.1090/S0002-9947-1948-0027263-2 |
| Reference:
|
[6] N. Bourbaki: General Topology, Part 1.Addison-Wesley Pub. Co., Don Mills, Ont., 1966 (translated from the French, Topologie Générale, Hermann, Paris). Zbl 0301.54001 |
| Reference:
|
[7] P. Conrad: Lex-subgroups of lattice-ordered groups.Czech. Math. J. 18 (1968), pp. 86-103. Zbl 0155.05902, MR 0225697 |
| Reference:
|
[8] W. Doyle: An arithmetical theorem for partially ordered sets.Bull. Amer. Math. Soc. 56 (1950), p. 366. |
| Reference:
|
[9] O. Frink: Topology in lattices.Trans. Amer. Math. Soc. 51 (1942), pp. 569-582. Zbl 0061.39305, MR 0006496, 10.1090/S0002-9947-1942-0006496-X |
| Reference:
|
[10] O. Frink: Ideals in partially ordered sets.Amer. Math. Monthly 61 (1954), pp. 223 - 234. Zbl 0055.25901, MR 0061575, 10.1080/00029890.1954.11988449 |
| Reference:
|
[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. MR 0102484 |
| Reference:
|
[12] C. Holland: The interval topology of a certain $l$-group.Czech. Math. J. 15 (1965), pp. 311-314. Zbl 0137.25702, MR 0177044 |
| Reference:
|
[13] J. Jakubík: The interval topology of an $l$-group.Coll. Math. 11 (1963), pp. 65-72. MR 0160831, 10.4064/cm-11-1-65-72 |
| Reference:
|
[14] J. L. Kelley: General Topology.D. van Nostrand Co., Inc., Princeton, 1955. Zbl 0066.16604, MR 0070144 |
| Reference:
|
[15] J. D. Lawson: Intrinsic lattice and semilattice topologies.Proceedings of the Conference on Lattice Theory (1973), University of Houston, to аррeаr. Zbl 0293.06011, MR 0401576 |
| Reference:
|
[16] R. J. Loy J. B. Miller: Tight Riesz Groups.J. Australian Math. Soc. 13 (1972), pp. IIA-IAO. MR 0297669 |
| Reference:
|
[17] H. Mayer M. Novotný: On some topologies on products of ordered sets.Arch. Math. (Brno) 1 (1965), pp. 251-257. MR 0195071 |
| Reference:
|
[18] T. Naito: Lattices with $P$-ideal topologies.Tohoku Math. J. (2) 12 (1960), pp. 235-262. Zbl 0094.01801, MR 0121319, 10.2748/tmj/1178244439 |
| Reference:
|
[19] R. H. Redfield: A topology for a lattice-ordered group.Trans. Amer. Math. Soc. 187 (1974), pp. 103-125. Zbl 0302.06028, MR 0327607, 10.1090/S0002-9947-1974-0327607-3 |
| Reference:
|
[20] B. С. Rennie: Lattices.Proc. Lon. Math. Soc. 52 (1951), pp. 386-400. Zbl 0044.37901, MR 0690634 |
| Reference:
|
[21] B. C. Rennie: Lattices.Foister & Jagg, Cambridge, 1952. |
| Reference:
|
[22] F. Šik: Zur Theorie der halbgeordnete Gruppen.Czech. Math. J. 6 (1956), pp. 1 - 25. MR 0081907 |
| Reference:
|
[23] A. J. Ward: On relations between certain intrinsic topologies in partially ordered sets.Proc. Cambridge Phil. Soc. 51 (1955), pp. 254-261. Zbl 0066.02101, MR 0070995 |
| . |
