Spaces of Abstract Events

被引：7

作者：

Chajda, Ivan ^{[1
]}

Laenger, Helmut ^{[2
]}

机构：

[1] Palacky Univ, Fac Sci, Dept Algebra & Geometry, Olomouc 77146, Czech Republic

[2] Vienna Univ Technol, Inst Discrete Math & Geometry, Fac Math & Geoinformat, A-1040 Vienna, Austria

来源：

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2013年 / 52卷 / 06期

关键词：

Numerical event; Abstract event; Orthomodular poset; Effect algebra; State; Full set of states; Antitone involution; Sectionally antitone involutions; Orthomodular lattice; EFFECT ALGEBRAS; PROBABILITIES;

D O I：

10.1007/s10773-012-1275-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We generalize the concept of a space of numerical events in such a way that this generalization corresponds to arbitrary orthomodular posets whereas spaces of numerical events correspond to orthomodular posets having a full set of states. Moreover, we show that there is a natural one-to-one correspondence between orthomodular posets and certain posets with sectionally antitone involutions. Finally, we characterize orthomodular lattices among orthomodular posets.

引用

下载

页码：1818 / 1824

页数：7

共 50 条

[1] Spaces of Abstract Events
Ivan Chajda
Helmut Länger
International Journal of Theoretical Physics, 2013, 52 : 1818 - 1824
[2] Abstract spaces
Tychonoff, A
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1926, 182 : 1519 - 1520
[3] Theory of abstract spaces. Abstract spaces with refined connections.
Potier, R
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1938, 206 : 1868 - 1870
[4] OPTIMIZATION IN ABSTRACT SPACES
TRUDZIK, LI
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1984, 29 (01) : 141 - 143
[5] ABSTRACT ANALYTIC SPACES
GECHE, FI
DOKLADY AKADEMII NAUK SSSR, 1974, 217 (06): : 1252 - 1255
[6] Projections in abstract spaces
Torrance, CC
ANNALS OF MATHEMATICS, 1936, 37 : 635 - 641
[7] INTEGRATION IN ABSTRACT SPACES
HILDEBRANDT, TH
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 59 (02) : 111 - 139
[8] ABSTRACT HARDY SPACES
Liu, Yin
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2022, 25 (02): : 477 - 493
[9] PROXIMITIES AND ABSTRACT SPACES
GASTL, GC
ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1969, 46 (04): : 395 - &
[10] CONCERNING ABSTRACT SPACES
ESTILL, ME
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 55 (09) : 875 - 875

← 1 2 3 4 5 →