Geodesic
Dense subsets of ordered sets
Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 571-579

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
Some modifications of the definition of density of subsets in ordered (= partially ordered) sets are given and the corresponding concepts are compared.
Some modifications of the definition of density of subsets in ordered (= partially ordered) sets are given and the corresponding concepts are compared.
DOI : 10.21136/MB.2001.134202
Classification : 06A06
Keywords: ordered set; weakly dense subset; dense subset; separability 
Novák, Vítězslav; Vránová, Lidmila. Dense subsets of ordered sets. Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 571-579. doi: 10.21136/MB.2001.134202
@article{10_21136_MB_2001_134202,
     author = {Nov\'ak, V{\'\i}t\v{e}zslav and Vr\'anov\'a, Lidmila},
     title = {Dense subsets of ordered sets},
     journal = {Mathematica Bohemica},
     pages = {571--579},
     year = {2001},
     volume = {126},
     number = {3},
     doi = {10.21136/MB.2001.134202},
     mrnumber = {1970260},
     zbl = {0979.06002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134202/}
}
TY  - JOUR
AU  - Novák, Vítězslav
AU  - Vránová, Lidmila
TI  - Dense subsets of ordered sets
JO  - Mathematica Bohemica
PY  - 2001
SP  - 571
EP  - 579
VL  - 126
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134202/
DO  - 10.21136/MB.2001.134202
LA  - en
ID  - 10_21136_MB_2001_134202
ER  - 
%0 Journal Article
%A Novák, Vítězslav
%A Vránová, Lidmila
%T Dense subsets of ordered sets
%J Mathematica Bohemica
%D 2001
%P 571-579
%V 126
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134202/
%R 10.21136/MB.2001.134202
%G en
%F 10_21136_MB_2001_134202

[1] G. Birkhoff: Generalized Arithmetic. Duke Math. J. 9 (1942), 283–302. | MR | Zbl

[2] G. Birkhoff: Lattice Theory. Third edition, Providence, Rhode Island, 1967. | MR | Zbl

[3] F. Hausdorff: Grundzüge der Mengenlehre. Leipzig, 1914.

[4] D. Kurepa: Partitive sets and ordered chains. Rad. Jug. Akad. Znan. Umjet, Odjel Mat. Fiz. Techn. Nauke 6 (1957), 197–235. | MR | Zbl

[5] V. M. Micheev: On sets containing the greatest number of pairwise incomparable Boole vectors. Probl. Kib. 2 (1959), 69–71. (Russian) | MR

[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

[7] J. Novák: On some characteristics of an ordered continuum. Czechoslovak Math. J. 2 (1952), 369–386. (Russian) | MR

[8] V. Novák: On the pseudodimension of ordered sets. Czechoslovak Math. J. 13 (1963), 587–598. | MR

[9] V. Novák: On the $\omega _\nu $-dimension and $\omega _\nu $-pseudodimension of ordered sets. Z. Math. Logik Grundlagen Math. 10 (1964), 43–48. | DOI | MR

[10] V. Novák: Some cardinal characteristics of ordered sets. Czechoslovak Math. J. 48 (1998), 135–144. | DOI | MR

[11] M. Novotný: On a certain characteristic of an ordered continuum. Czechoslovak Math. J. 3 (1953), 75–82. (Russian)

[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

[13] M. Novotný: Bemerkung über die Darstellung teilweise geordneter Mengen. Spisy přír. fak. MU Brno 389 (1955), 451–458. | MR

[14] J. Schmidt: Zur Kennzeichnung der Dedekind-Mac Neilleschen Hülle einer geordneten Menge. Arch. Math. 7 (1956), 241–249. | DOI | MR

[15] E. Sperner: Ein Satz über Untermengen einer endlichen Menge. Math. Z. 27 (1928), 554–558. | MR

Cité par Sources :