Szlenk and w^⁎-dentability indices of C(K)

详细信息    查看全文

• 作者：R.M. Causey ^{causeyrm@miamioh.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Szlenk index ; Dentability index
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：834-845
• 全文大小：375 K

文摘

Given any compact, Hausdorff space K   and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=025423f6ec5c4353f8a17e02fda5a15c" title="Click to view the MathML source">1<p<∞class="mathContainer hidden">class="mathCode">$1<p<\infty$, we compute the Szlenk and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si2.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=f3ab4836e0a14df4ab4290550ad15f22" title="Click to view the MathML source">w^⁎class="mathContainer hidden">class="mathCode">$w^{⁎}$-dentability indices of the spaces class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si3.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=6e40aa03ed14c811aaec00298964abc5" title="Click to view the MathML source">C(K)class="mathContainer hidden">class="mathCode">$C(K)$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si4.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=5eb4e1233390f0c225fab5bced1b822f" title="Click to view the MathML source">L_p(C(K))class="mathContainer hidden">class="mathCode">$L_p(C(K))$. We show that if K   is compact, Hausdorff, scattered, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si5.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=79c60df45187652e54da58783deac1d5" title="Click to view the MathML source">CB(K)class="mathContainer hidden">class="mathCode">$CB(K)$ is the Cantor–Bendixson index of K, and ξ   is the minimum ordinal such that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si342.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=dc9089f33ef2453c6e383c9aa2228ea3" title="Click to view the MathML source">CB(K)⩽ω^ξclass="mathContainer hidden">class="mathCode">$CB(K)⩽{\omega }^{\xi }$, then class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si7.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=38c39d7f80a4b5f8c0c2621348a7b6f3" title="Click to view the MathML source">Sz(C(K))=ω^ξclass="mathContainer hidden">class="mathCode">$Sz(C(K))={\omega }^{\xi }$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306278&_mathId=si8.gif&_user=111111111&_pii=S0022247X16306278&_rdoc=1&_issn=0022247X&md5=2d8030d0aaee2d9e3b0088d90e7e6c84" title="Click to view the MathML source">Dz(C(K))=Sz(L_p(C(K)))=ω^1+ξclass="mathContainer hidden">class="mathCode">$Dz(C(K))=Sz(L_p(C(K)))={\omega }^{1+\xi }$.