Pseudo-solenoids are not continuously homogeneous

详细信息    查看全文

• 作者：Frank Sturm¹ ; ^{fhs0001@auburn.edu" class="auth_mail}
• 关键词：Continuum theory ; Pseudo-circle ; Pseudo-solenoid ; Pseudo-arc ; Hereditarily indecomposable continua ; Inverse limits ; General homogeneity ; Open homogeneity ; Continuous homogeneity
• 刊名：Topology and its Applications
• 出版年：1 July 2014
• 年：2014
• 卷：171
• 期：Complete
• 页码：71-86
• 全文大小：411 K

文摘

The topological space X   is a pseudo-solenoid if X   is a hereditarily indecomposable, non-chainable, and circle-like continuum. It is shown that no such continuum is continuously homogeneous. Specifically, there are two points in X  , identified as z   and class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864114001254&_mathId=si1.gif&_user=111111111&_pii=S0166864114001254&_rdoc=1&_issn=01668641&md5=3985b3b2fec25bed1e10fdfdaf849a15">class="imgLazyJSB inlineImage" height="13" width="9" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0166864114001254-si1.gif">class="mathContainer hidden">class="mathCode">$\overline{1}$, such that for any continuous surjection class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864114001254&_mathId=si2.gif&_user=111111111&_pii=S0166864114001254&_rdoc=1&_issn=01668641&md5=c09be070b6db1c2b31662789416c63f2" title="Click to view the MathML source">f:X→Xclass="mathContainer hidden">class="mathCode">$f:X\to X$, class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864114001254&_mathId=si3.gif&_user=111111111&_pii=S0166864114001254&_rdoc=1&_issn=01668641&md5=a98a4c0300162a899f9f0ed0476e162a">class="imgLazyJSB inlineImage" height="17" width="60" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0166864114001254-si3.gif">class="mathContainer hidden">class="mathCode">$f(\overline{1})\ne z$. This answers a question of J.J. Charatonik in the negative.