Cleavability over ordinals

被引：0

作者：

Levine, Shari ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX1 3LB, England

来源：

TOPOLOGY AND ITS APPLICATIONS | 2013年 / 160卷 / 12期

关键词：

Cleavability; Linearly ordered topological space (LOTS); Ordinal; Homeomorphism;

D O I：

10.1016/j.topol.2013.05.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we show that if X is an infinite compactum cleavable over an ordinal, then X must be homeomorphic to an ordinal. X must also therefore be a LOTS. This answers two fundamental questions in the area of cleavability. We also leave it as an open question whether cleavability of an infinite compactum X over an ordinal lambda implies X is embeddable into lambda. (C) 2013 Published by Elsevier B.V.

引用

页码：1456 / 1465

页数：10

共 14 条

[1] [Anonymous], 1920, Fund. Math, DOI DOI 10.4064/FM-1-1-17-27
[2] Arhangel'skii A.V., 1992, ANN NY ACAD SCI, V659, P18
[3] A SURVEY OF CLEAVABILITY
ARHANGELSKII, AV
[J]. TOPOLOGY AND ITS APPLICATIONS, 1993, 54 (1-3) : 141 - 163
[4] Arkhangel'skii A.V., 1990, J SOVIET MATH, V50, P1497
[5] On cleavability of continua over LOTS
Buzyakova, RZ
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (07) : 2171 - 2181
[6] Hewitt E., 1943, Duke Math. J, V10, P309, DOI DOI 10.1215/S0012-7094-43-01029-4
[7] Kunen K., 1980, Set theory, Studies in Logic and the Foundations of Mathematics, V102
[8] Cleavability over scattered first-countable LOTS
Levine, Shari
[J]. TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (15) : 3300 - 3306
[9] Cleavability and scattered sets of non-trivial fibers
Levine, Shari
[J]. TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (14) : 3171 - 3179
[10] SEPARABILITY, COUNTABLE CHAIN CONDITION AND LINDELOF PROPERTY IN LINEARLY ORDERABLE SPACES
LUTZER, DJ
BENNETT, HR
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 23 (03) : 664 - &

← 1 2 →