Baire theorem for ideals of sets

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• 作者：A. Avilé ; s^a ; ^{avileslo@um.es" class="auth_mail" title="E-mail the corresponding author} ; V. Kadets^b ; ^{v.kateds@karazin.ua" class="auth_mail" title="E-mail the corresponding author} ; A. Pé ; rez^a ; ^{antonio.perez7@um.es" class="auth_mail" title="E-mail the corresponding author} ; S. Solecki^c ; ^{ssolecki@math.uiuc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Baire theorem ; Ideal of sets ; Nowhere dense ; Analytic set
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1221-1231
• 全文大小：379 K

文摘

We study ideals 47X1600216X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=64cf6f8988127ebc00de3b0bde3e3830" title="Click to view the MathML source">I$\mathcal{I}$ on 47X1600216X&_mathId=si2.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=2a07a14b254e0eb644aea6a1acbefe10" title="Click to view the MathML source">N$\mathbb{N}$ satisfying the following Baire-type property: if X is a complete metric space and  47X1600216X&_mathId=si3.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=9fa2099f970228f980dddb4169ec4b0e" title="Click to view the MathML source">{X_A:A∈I}$\{X_A:A\in \mathcal{I}\}$is a family of nowhere dense subsets of X with  47X1600216X&_mathId=si4.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=312139aa46fb471b7eab9d34cda78816" title="Click to view the MathML source">X_A⊂X_B$X_A\subset X_B$whenever  47X1600216X&_mathId=si5.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=bfe7e1440d2005bd11cbc6037ae998e3" title="Click to view the MathML source">A⊂B$A\subset B$, then  47X1600216X&_mathId=si6.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=ed091ffe1b47681abc93273ea8a6f693" title="Click to view the MathML source">⋃_A∈IX_A≠X${\bigcup }_{A\in \mathcal{I}}{X}_A\ne X$. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of X.