Ultrafilter Convergence in Ordered Topological Spaces

被引：0

作者：

Lipparini, Paolo ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, Viale Ordini Sci, I-00133 Rome, Italy

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2016年 / 33卷 / 02期

关键词：

Linearly ordered; Generalized ordered topological space; Ultrafilter convergence; Compactness; Pseudocompactness; (pseudo-)gap; Converging.-sequence; (weak) [nu.nu]-compactness; (weak) initial lambda-compactness; Complete accumulation point; lambda-boundedness; Decomposable; Descendingly complete; Regular ultrafilter; COMPACT;

D O I：

10.1007/s11083-015-9365-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter D, the notions of D-compactness and of D-pseudocompactness are equivalent. Any product of initially lambda-compact generalized ordered topological spaces is still initially lambda-compact. On the other hand, preservation under products of certain compactness properties is independent from the usual axioms for set theory.

引用

页码：269 / 287

页数：19

共 28 条

[1]

Alexandroff P., 1929, VERHANDELINGEN AMSTE, V14, P93

[2]

[Anonymous], 1990, STUDIES LOGIC FDN MA

[3]

[Anonymous], 2012, TOPOL P

[4] ON BOX, WEAK BOX AND STRONG COMPACTNESS [J].

APTER, AW ;

HENLE, JM .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1992, 24 :513-518

[5] THE WEAK CLASS-STAR IS REALLY WEAKER THAN THE FULL-CLASS [J].

BENDAVID, S ;

MAGIDOR, M .

JOURNAL OF SYMBOLIC LOGIC, 1986, 51 (04) :1029-1033

[6]

Bennett HR, 2002, RECENT PROGRESS IN GENERAL TOPOLOGY II, P83, DOI 10.1016/B978-044450980-2/50003-0

[7]

Bernstein A. I., 1970, FUND MATH, V66, P185

[8]

Caicedo X., 1999, SYNTHESE LIB, V280, P131

[9] REGULARITY OF ULTRAFILTERS AND THE CORE MODEL [J].

DONDER, HD .

ISRAEL JOURNAL OF MATHEMATICS, 1988, 63 (03) :289-322

[10]

GARCIAFERREIRA S, 2001, TOPOLOGY P, V24, P149

← 1 2 3 →