EMBEDDING OF PARTIALLY ORDERED TOPOLOGICAL SPACES IN FELL TOPOLOGICAL HYPERSPACES

被引：0

作者：

Li, Jinlu ^{[1
]}

Wang, Yuehu ^{[2
]}

Wen, Ching-Feng ^{[3
,4
,5
]}

Yao, Jen-Chih ^{[6
]}

Zhang, Congjun ^{[7
]}

机构：

[1] Shawnee State Univ, Dept Math, Portsmouth, OH 45662 USA

[2] Nanjing Univ Finance & Econ, Sch Management Sci & Engn, Nanjing 210023, Peoples R China

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80708, Taiwan

[4] Kaohsiung Med Univ, Res Ctr Nonlinear Anal & Optimizat, Kaohsiung 80708, Taiwan

[5] Kaohsiung Med Univ, Dept Med Res, Kaohsiung Med Univ Hosp, Kaohsiung 80708, Taiwan

[6] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung, Taiwan

[7] Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing 210023, Peoples R China

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2023年 / 24卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Partially ordered topological space; hyperspace; Fell topology; Vietoris topology; topological order-embedding; LATTICES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove a theorem about embedding of some partially ordered topological spaces in topological hyperspaces equipped with Fell topology. Then we give some examples to show that the map defining the embedding may not be continuous with respect to Vietoris topology or Hausdorff topology equipped on the hyperspaces.

引用

页码：2119 / 2142

页数：24

共 25 条

[1]

Anderson L., 1959, Proc. Amer. Math. Soc., V10, P715

[2]

[Anonymous], 2001, Handbook of Metric Fixed Point Theory

[3] METRIC-SPACES WITH NICE CLOSED BALLS AND DISTANCE FUNCTIONS FOR CLOSED-SETS [J].

BEER, G .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1987, 35 (01) :81-96

[4] DISTANCE FUNCTIONALS AND SUPREMA OF HYPERSPACE TOPOLOGIES [J].

BEER, G ;

LECHICKI, A ;

LEVI, S ;

NAIMPALLY, S .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1992, 162 :367-381

[5]

Beer G., 1993, TOPOLOGIES CLOSED CL

[6]

Bezhanishvili G, 2011, HOUSTON J MATH, V37, P699

[7]

Bridges D.S., 1995, Representations of Preference Orderings, DOI DOI 10.1007/978-3-642-51495-1

[8] SEPARATION AXIOMS FOR CERTAIN TYPES OF ORDERED TOPOLOGICAL-SPACE [J].

BURGESS, DCJ ;

FITZPATRICK, M .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1977, 82 (JUL) :59-65

[9] A NOTE ON PARTIALLY ORDERED COMPACTA [J].

CARRUTH, JH .

PACIFIC JOURNAL OF MATHEMATICS, 1968, 24 (02) :229-&

[10] EMBEDDING ORDERED TOPOLOGICAL-SPACES INTO TOPOLOGICAL SEMI-LATTICES [J].

CHOE, TH ;

PARK, YS .

SEMIGROUP FORUM, 1979, 17 (03) :189-199

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