| Title:
|
Dense subsets of ordered sets (English) |
| Author:
|
Novák, Vítězslav |
| Author:
|
Vránová, Lidmila |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
571-579 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some modifications of the definition of density of subsets in ordered (= partially ordered) sets are given and the corresponding concepts are compared. (English) |
| Keyword:
|
ordered set |
| Keyword:
|
weakly dense subset |
| Keyword:
|
dense subset |
| Keyword:
|
separability |
| MSC:
|
06A06 |
| idZBL:
|
Zbl 0979.06002 |
| idMR:
|
MR1970260 |
| DOI:
|
10.21136/MB.2001.134202 |
| . |
| Date available:
|
2009-09-24T21:54:23Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134202 |
| . |
| Reference:
|
[1] G. Birkhoff: Generalized Arithmetic.Duke Math. J. 9 (1942), 283–302. Zbl 0060.12609, MR 0007031 |
| Reference:
|
[2] G. Birkhoff: Lattice Theory.Third edition, Providence, Rhode Island, 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[3] F. Hausdorff: Grundzüge der Mengenlehre.Leipzig, 1914. |
| Reference:
|
[4] D. Kurepa: Partitive sets and ordered chains.Rad. Jug. Akad. Znan. Umjet, Odjel Mat. Fiz. Techn. Nauke 6 (1957), 197–235. Zbl 0147.26301, MR 0097328 |
| Reference:
|
[5] V. M. Micheev: On sets containing the greatest number of pairwise incomparable Boole vectors.Probl. Kib. 2 (1959), 69–71. (Russian) MR 0123498 |
| Reference:
|
[6] J. Novák: On some ordered continua of power $2^{\aleph _0}$ containing a dense subset of power $\aleph _1$.Czechoslovak Math. J. 1 (1951), 63–79. MR 0049262 |
| Reference:
|
[7] J. Novák: On some characteristics of an ordered continuum.Czechoslovak Math. J. 2 (1952), 369–386. (Russian) MR 0062197 |
| Reference:
|
[8] V. Novák: On the pseudodimension of ordered sets.Czechoslovak Math. J. 13 (1963), 587–598. MR 0180507 |
| Reference:
|
[9] V. Novák: On the $\omega _\nu $-dimension and $\omega _\nu $-pseudodimension of ordered sets.Z. Math. Logik Grundlagen Math. 10 (1964), 43–48. MR 0180508, 10.1002/malq.19640100204 |
| Reference:
|
[10] V. Novák: Some cardinal characteristics of ordered sets.Czechoslovak Math. J. 48 (1998), 135–144. MR 1614021, 10.1023/A:1022523830353 |
| Reference:
|
[11] M. Novotný: On a certain characteristic of an ordered continuum.Czechoslovak Math. J. 3 (1953), 75–82. (Russian) |
| Reference:
|
[12] M. Novotný: On representation of partially ordered sets by means of sequences of 0’s and 1’s.Čas. pěst. mat. 78 (1953), 61–64. (Czech) MR 0079066 |
| Reference:
|
[13] M. Novotný: Bemerkung über die Darstellung teilweise geordneter Mengen.Spisy přír. fak. MU Brno 389 (1955), 451–458. MR 0082958 |
| Reference:
|
[14] J. Schmidt: Zur Kennzeichnung der Dedekind-Mac Neilleschen Hülle einer geordneten Menge.Arch. Math. 7 (1956), 241–249. MR 0084484, 10.1007/BF01900297 |
| Reference:
|
[15] E. Sperner: Ein Satz über Untermengen einer endlichen Menge.Math. Z. 27 (1928), 554–558. MR 1544925 |
| . |
